NCERT Solutions for Class 12 Maths Chapter 7 Integrals

NCERT Solutions for Class 12 Maths Chapter 7 Integrals provided here is extremely helpful in revising complete syllabus and getting a strong base on it. NCERT 12th Class Maths Integrals all questions are solved with detailed explanation available for students. In this article we had given of NCERT solutions for Integrals Class 12 Maths step by step solution for each and every question of the chapter. These solutions will also help you with your homework. Best teachers across the India created NCERT solutions for Class 12 Maths Chapter 7 Integrals according to curriculum and pattern of syllabus as per guidelines of NCERT (CBSE) Books.

Table of Contents

12th Class NCERT Maths Chapter 7 Integrals

Name of Organization	NCERT
Name of Class	12th Class
Name of Subject	Maths
Name of Chapter	Chapter 7
Name of Content	Integrals
Name of Category	NCERT Solutions
Official site	http://ncert.nic.in/

Chapter 7 Integrals covers numerous Questions and answers from all topics and sub-topics which are given below

Section Name	Topic Name
7	Integrals
7.1	Introduction
7.2	Integration as an Inverse Process of Differentiation
7.3	Methods of Integration
7.4	Integrals of some Particular Functions
7.5	Integration by Partial Fractions
7.6	Integration by Parts
7.7	Definite Integral
7.8	Fundamental Theorem of Calculus
7.9	Evaluation of Definite Integrals by Substitution
7.10	Some Properties of Definite Integrals

Integrals Ex 7.1 Class 12

Ex 7.1 Class 12 Maths Question 1.
sin 2x
Solution:
Class 12 Integrals NCERT Solutions Ex 7.1 Q 1
Ex 7.1 Class 12 Maths Question 2.
cos 3x
Solution:

Ex 7.1 Class 12 Maths Question 3.
${ e }^{ 2x }$
Solution:

Ex 7.1 Class 12 Maths Question 4.
(ax + c)²
Solution:

Ex 7.1 Class 12 Maths Question 5.
${ sin\quad 2x-4e }^{ 3x }$
Ex 7.1 Class 12 Maths Solution:
Class 12 Integrals NCERT Solutions Ex 7.1 Q 5
Find the following integrals in Exercises 6 to 20 :

Ex 7.1 Class 12 Maths Question 6.
$\int { \left( { 4e }^{ 3x }+1 \right) dx }$
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.1 Q 6
Ex 7.1 Class 12 Maths Question 7.
$\int { { x }^{ 2 }\left( 1-\frac { 1 }{ { x }^{ 2 } } \right) dx }$
Solution:

Ex 7.1 Class 12 Maths Question 8.
$\int { { (ax }^{ 2 }+bx+c)dx }$
Solution:

Ex 7.1 Class 12 Maths Question 9.
$\int { \left( { 2x }^{ 2 }+{ e }^{ x } \right) dx }$
Solution:
Integrals Class 12 NCERT Solutions Chapter 7 Ex 7.1 Q 9
Ex 7.1 Class 12 Maths Question 10.
$\int { { \left[ \sqrt { x } -\frac { 1 }{ \sqrt { x } } \right] }^{ 2 }dx }$
Solution:

Ex 7.1 Class 12 Maths Question 11.
$\int { \frac { { x }^{ 3 }+{ 5x }^{ 2 }-4 }{ { x }^{ 2 } } dx }$
Solution:
Integrals Class 12 NCERT Solutions Chapter 7 Ex 7.1 Q 11
Ex 7.1 Class 12 Maths Question 12.
$\int { \frac { { x }^{ 3 }+3x+4 }{ \sqrt { x } } dx }$
Solution:
Integration Class 12 NCERT Solutions Chapter 7 Ex 7.1 Q 12
Ex 7.1 Class 12 Maths Question 13.
$\int { \frac { { x }^{ 3 }-{ x }^{ 2 }+x-1 }{ x-1 } dx }$
Solution:

Ex 7.1 Class 12 Maths Question 14.
$\int { \left( 1-x \right) \sqrt { x } dx }$
Solution:
Class 12 Maths NCERT Solutions Chapter 7 Ex 7.1 Q 14
Ex 7.1 Class 12 Maths Question 15.
$\int { \sqrt { x } \left( { 3x }^{ 2 }+2x+3 \right) dx }$
Solution:

Ex 7.1 Class 12 Maths Question 16.
$\int { (2x-3cosx+{ e }^{ x })dx }$
Solution:
Maths NCERT Class 12 Solutions Chapter 7 Integrals Ex 7.1 Q 16
Ex 7.1 Class 12 Maths Question 17.
$\int { \left( { 2x }^{ 2 }-3sinx+5\sqrt { x } \right) dx }$
Solution:

Ex 7.1 Class 12 Maths Question 18.
$\int { secx(secx+tanx)dx }$
Solution:

Ex 7.1 Class 12 Maths Question 19.
$\int { \frac { { sec }^{ 2 }x }{ { cosec }^{ 2 }x } dx }$
Solution:
Integration Class 12 NCERT Solutions Chapter 7 Ex 7.1 Q 19
Ex 7.1 Class 12 Maths Question 20.
$\int { \frac { 2-3sinx }{ { cos }^{ 2 }x } dx }$
Solution:

Choose the correct answer in Exercises 21 and 22.
Ex 7.1 Class 12 Maths Question 21.
The antiderivative $\left( \sqrt { x } +\frac { 1 }{ \sqrt { x } } \right)$ equals
(a) $\frac { 1 }{ 3 } { x }^{ \frac { 1 }{ 3 } }+{ 2x }^{ \frac { 1 }{ 2 } }+c$
(b) $\frac { 2 }{ 3 } { x }^{ \frac { 2 }{ 3 } }+{ \frac { 1 }{ 2 } x }^{ 2 }+c$
(c) $\frac { 2 }{ 3 } { x }^{ \frac { 3 }{ 2 } }+{ 2x }^{ \frac { 1 }{ 2 } }+c$
(d) $\frac { 3 }{ 2 } { x }^{ \frac { 3 }{ 2 } }+\frac { 1 }{ 2 } { x }^{ \frac { 1 }{ 2 } }+c$
Solution:
Integration Class 12 NCERT Solutions Chapter 7 Ex 7.1 Q 21
Ex 7.1 Class 12 Maths Question 22.
If $\frac { d }{ dx } f(x)={ 4x }^{ 3 }-\frac { 3 }{ { x }^{ 4 } }$ such that f(2)=0 then f(x) is
(a) ${ x }^{ 4 }+\frac { 1 }{ { x }^{ 3 } } -\frac { 129 }{ 8 }$
(b) ${ x }^{ 3 }+\frac { 1 }{ { x }^{ 4 } } +\frac { 129 }{ 8 }$
(c) ${ x }^{ 4 }+\frac { 1 }{ { x }^{ 3 } } +\frac { 129 }{ 8 }$
(d) ${ x }^{ 3 }+\frac { 1 }{ { x }^{ 4 } } -\frac { 129 }{ 8 }$
Solution:
Integration Class 12 NCERT Solutions Chapter 7 Ex 7.1 Q 22

Move to Top → Class 12 Integrals Chapter 7

Integrals Ex 7.2 Class 12

Integrate the functions in Exercises 1 to 37:

Ex 7.2 Class 12 Maths Question 1.
$\frac { 2x }{ 1+{ x }^{ 2 } }$
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.2 Q 1
Ex 7.2 Class 12 Maths Question 2.
$\frac { { \left( logx \right) }^{ 2 } }{ x }$
Solution:

Ex 7.2 Class 12 Maths Question 3.
$\frac { 1 }{ x+xlogx }$
Solution:

Ex 7.2 Class 12 Maths Question 4.
sinx sin(cosx)
Solution:
ncert solutions class 12 maths Chapter 7 Integrals Ex 7.2 Q 4
Ex 7.2 Class 12 Maths Question 5.
sin(ax+b) cos(ax+b)
Solution:
class 12 integration NCERT Solutions Chapter 7 Ex 7.2 Q 5
Ex 7.2 Class 12 Maths Question 6.
$\sqrt { ax+b }$
Solution:

Ex 7.2 Class 12 Maths Question 7.
$x\sqrt { x+2 }$
Solution:

Ex 7.2 Class 12 Maths Question 8.
$x\sqrt { 1+{ 2x }^{ 2 } }$
Solution:
class 12 maths integration NCERT Solutions Chapter 7 Ex 7.2 Q 8

Ex 7.2 Class 12 Maths Question 9.
$(4x+2)\sqrt { { x }^{ 2 }+x+1 }$
Solution:
class 12 maths integration NCERT Solutions Chapter 7 Ex 7.2 Q 9
Ex 7.2 Class 12 Maths Question 10.
$\frac { 1 }{ x-\sqrt { x } }$
Solution:

Ex 7.2 Class 12 Maths Question 11.
$\frac { x }{ \sqrt { x+4 } } ,x>0$
Solution:

Ex 7.2 Class 12 Maths Question 12.
${ { (x }^{ 3 }-1) }^{ \frac { 1 }{ 3 } }.{ x }^{ 5 }$
Solution:
ncert class 12 maths solutions Integrals Ex 7.2 Q 12
Ex 7.2 Class 12 Maths Question 13.
$\frac { { x }^{ 2 } }{ { { (2+3x }^{ 3 }) }^{ 3 } }$
Solution:

Ex 7.2 Class 12 Maths Question 14.
$\frac { 1 }{ x(logx)^{ m } } ,x>0$
Solution:

Ex 7.2 Class 12 Maths Question 15.
$\frac { x }{ 9-4{ x }^{ 2 } }$
Solution:
ncert class 12 maths solutions Integrals Ex 7.2 Q 14
Ex 7.2 Class 12 Maths Question 16.
${ e }^{ 2x+3 }$
Solution:
ncert maths solutions class 12 Integration Chapter 7 Ex 7.2 Q 16
Ex 7.2 Class 12 Maths Question 17.
$\frac { x }{ { e }^{ { x }^{ 2 } } }$
Solution:

Ex 7.2 Class 12 Maths Question 18.
$\frac { { e }^{ { tan }^{ -1 }x } }{ 1+{ x }^{ 2 } }$
Solution:

Ex 7.2 Class 12 Maths Question 19.
$\frac { { e }^{ 2x }-1 }{ { e }^{ 2x }+1 }$
Solution:
integration ncert solutions Class 12 chapter 7 Ex 7.2 Q 19
Ex 7.2 Class 12 Maths Question 20.
$\frac { { e }^{ 2x }-{ e }^{ 2x } }{ { e }^{ 2x }+{ e }^{ -2x } }$
Solution:

Ex 7.2 Class 12 Maths Question 21.
tan²(2x-3)
Solution:
∫tan²(2x-3)dx = ∫[sec²(2x-3)-1]dx = I
put 2x-3 = t
so that 2dx = dt
I = $\frac { 1 }{ 2 }$ ∫sec²t dt-x+c
= $\frac { 1 }{ 2 }t-x+c$
= $\frac { 1 }{ 2 }tan(2x-3)-x+c$
Ex 7.2 Class 12 Maths Question 22.
sec²(7-4x)
Solution:
maths class 12 ncert solutions Chapter 7 Integration Ex 7.2 Q 22
Ex 7.2 Class 12 Maths Question 23.
$\frac { { sin }^{ -1 }x }{ \sqrt { 1-{ x }^{ 2 } } }$
Solution:

Ex 7.2 Class 12 Maths Question 24.
$\frac { 2cosx-3sinx }{ 6cosx+4sinx }$
Solution:
Ex 7.2 class 12 maths NCERT Solutions Q 24
Ex 7.2 Class 12 Maths Question 25.
$\frac { 1 }{ { cos }^{ 2 }x{ (1-tanx) }^{ 2 } }$
Solution:

Ex 7.2 Class 12 Maths Question 26.
$\frac { cos\sqrt { x } }{ \sqrt { x } }$
Solution:

Ex 7.2 Class 12 Maths Question 27.
$\sqrt { sin2x } cos2x$
Solution:
Ex 7.2 class 12 maths NCERT Solutions Q 27
Ex 7.2 Class 12 Maths Question 28.
$\frac { cosx }{ \sqrt { 1+sinx } }$
Solution:
Integration Solutions class 12 Maths Chapter 7 Ex 7.2 Q 28
Ex 7.2 Class 12 Maths Question 29.
cotx log sinx
Solution:

Ex 7.2 Class 12 Maths Question 30.
$\frac { sinx }{ 1+cosx }$
Solution:

Ex 7.2 Class 12 Maths Question 31.
$\frac { sinx }{ { (1+cosx) }^{ 2 } }$
Solution:
NCERT Maths Class 12 Solutions Chapter 7 Ex 7.2 Q 31
Ex 7.2 Class 12 Maths Question 32.
$\frac { 1 }{ 1+cotx }$
Solution:

Ex 7.2 Class 12 Maths Question 33.
$\frac { 1 }{ 1-tanx }$
Solution:

Ex 7.2 Class 12 Maths Question 34.
$\frac { \sqrt { tanx } }{ sinxcosx }$
Solution:
NCERT Integration Solutions Ex 7.2 Q 34
Ex 7.2 Class 12 Maths Question 35.
$\frac { { (1+logx) }^{ 2 } }{ x }$
Solution:

Ex 7.2 Class 12 Maths Question 36.
$\frac { (x+1){ (x+logx) }^{ 2 } }{ x }$
Solution:

Ex 7.2 Class 12 Maths Question 37.
$\frac { { x }^{ 3 }sin({ tan }^{ -1 }{ x }^{ 4 }) }{ 1+{ x }^{ 8 } } dx$
Solution:
NCERT Integration Solutions Ex 7.2 Q 37
Choose the correct answer in exercises 38 and 39

Ex 7.2 Class 12 Maths Question 38.
$\int { \frac { { 10x }^{ 9 }+{ 10 }^{ x }log{ e }^{ 10 } }{ { x }^{ 10 }+{ 10 }^{ x } } dx }$
(a) 10x – x10 + C
(b) 10x + x10 + C
(c) (10x – x10) + C
(d) log (10x + x10) + C
Solution:
NCERT Integration Solutions Ex 7.2 Q 38
Ex 7.2 Class 12 Maths Question 39.
$\int { \frac { dx }{ { sin }^{ 2 }x{ \quad cos }^{ 2 }x } = }$
(a) tanx + cotx + c
(b) tanx – cotx + c
(c) tanx cotx + c
(d) tanx – cot2x + c
Solution:
NCERT Solutions for Class 12 Maths integrals Ex 7.2 Q 39

Move to Top → Class 12 Integrals Chapter 7

Integrals Ex 7.3 Class 12

Find the integrals of the functions in Exercises 1 to 22.
Ex 7.3 Class 12 Maths Question 1.
sin²(2x+5)
Solution:
Ex 7.3 Class 12 Maths NCERT Solutions Q 1
Ex 7.3 Class 12 Maths Question 2.
sin3x cos4x
Solution:

Ex 7.3 Class 12 Maths Question 3.
∫cos2x cos4x cos6x dx
Solution:

Ex 7.3 Class 12 Maths Question 4.
∫sin³(2x+1)dx
Solution:

Ex 7.3 Class 12 Maths Question 5.
sin³x cos³x
Solution:
NCERT Solutions Integration Chapter 7 Ex 7.3 Q 5
Ex 7.3 Class 12 Maths Question 6.
sinx sin2x sin3x
Solution:

Ex 7.3 Class 12 Maths Question 7.
sin 4x sin 8x
Solution:

Ex 7.3 Class 12 Maths Question 8.
$\frac { 1-cosx }{ 1+cosx }$
Solution:
chapter 7 maths class 12 NCERT Solutions Ex 7.3 Q 8
Ex 7.3 Class 12 Maths Question 9.
$\frac { cosx }{ 1+cosx }$
Solution:
Class 12 Maths Chapter 7 Solutions Ex 7.3 Q 9
Ex 7.3 Class 12 Maths Question 10.
∫sinx⁴ dx
Solution:

Ex 7.3 Class 12 Maths Question 11.
cos⁴ 2x
Solution:

Ex 7.3 Class 12 Maths Question 12.
$\frac { { sin }^{ 2 }x }{ 1+cosx }$
Solution:

Ex 7.3 Class 12 Maths Question 13.
$\frac { cos2x-cos2\alpha }{ cosx-cos\alpha }$
Solution:
Class 12 Maths Chapter 7 Solutions Ex 7.3 Q 13
Ex 7.3 Class 12 Maths Question 14.
$\frac { cosx-sinx }{ 1+sin2x }$
Solution:
Chapter 7 Class 12 Maths NCERT Solutions Ex 7.3 Q 14
Ex 7.3 Class 12 Maths Question 15.
$\int { { tan }^{ 3 }2x\quad sec2x\quad dx=I }$
Solution:

Ex 7.3 Class 12 Maths Question 16.
tan⁴x
Solution:
NCERT Solutions for Class 12 Maths Ex 7.3 Q 16
Ex 7.3 Class 12 Maths Question 17.
$\frac { { sin }^{ 3 }x+{ cos }^{ 3 }x }{ { sin }^{ 2 }x{ cos }^{ 2 }x }$
Solution:

Ex 7.3 Class 12 Maths Question 18.
$\frac { cos2x+{ 2sin }^{ 2 }x }{ { cos }^{ 2 }x }$
Solution:

Ex 7.3 Class 12 Maths Question 19.
$\frac { 1 }{ sinx{ cos }^{ 3 }x }$
Solution:
NCERT Solutions for Class 12 Maths Ex 7.3 Q 19
Ex 7.3 Class 12 Maths Question 20.
$\frac { cos2x }{ { (cosx+sinx) }^{ 2 } }$
Solution:
Class 12 Maths NCERT Solutions Chapter 7 Ex 7.3 Q 20
Ex 7.3 Class 12 Maths Question 21.
sin^-1 (cos x)
Solution:

Ex 7.3 Class 12 Maths Question 22.
$\int { \frac { 1 }{ cos(x-a)cos(x-b) } dx }$
Solution:

Ex 7.3 Class 12 Maths Question 23.
$\int { \frac { { sin }^{ 2 }x-{ cos }^{ 2 }x }{ { sin }^{ 2 }x{ cos }^{ 2 }x } } dx\quad is\quad equal\quad to$
(a) tanx+cotx+c
(b) tanx+cosecx+c
(c) -tanx+cotx+c
(d) tanx+secx+c
Solution:
NCERT Solution Class 12 Maths Ex 7.3 Q 23
Ex 7.3 Class 12 Maths Question 24.
$\int { \frac { e^{ x }(1+x) }{ cos^{ 2 }({ e }^{ x }.{ x }) } } dx\quad is\quad equal\quad to$
(a) -cot(e.x^x)+c
(b) tan(xe^x)+c
(c) tan(e^x)+c
(d) cot e^x+c
Solution:

Move to Top → Class 12 Integrals Chapter 7

Integrals Class 12 Ex 7.4

Ex 7.4 Class 12 Maths Question 1.
$\frac { { 3x }^{ 2 } }{ { x }^{ 6 }+1 }$
Solution:
Class 12 Integrals NCERT Solutions Ex 7.4 Q 1
Ex 7.4 Class 12 Maths Question 2.
$\frac { 1 }{ \sqrt { 1+{ 4x }^{ 2 } } }$
Solution:

Ex 7.4 Class 12 Maths Question 3.
$\frac { 1 }{ \sqrt { { (2-x) }^{ 2 }+1 } }$
Solution:

Ex 7.4 Class 12 Maths Question 4.
$\frac { 1 }{ \sqrt { 9-{ 25x }^{ 2 } } }$
Solution:
Class 12 Integrals NCERT Solutions Ex 7.4 Q 4
Ex 7.4 Class 12 Maths Question 5.
$\frac { 3x }{ 1+{ 2x }^{ 4 } }$
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 PDF Ex 7.4 Q 5
Ex 7.4 Class 12 Maths Question 6.
$\frac { { x }^{ 2 } }{ 1-{ x }^{ 6 } }$
Solution:

Ex 7.4 Class 12 Maths Question 7.
$\frac { x-1 }{ \sqrt { { x }^{ 2 }-1 } }$
Solution:

Ex 7.4 Class 12 Maths Question 8.
$\frac { { x }^{ 2 } }{ \sqrt { { x }^{ 6 }+{ a }^{ 6 } } }$
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 PDF Ex 7.4 Q 8
Ex 7.4 Class 12 Maths Question 9.
$\frac { { sec }^{ 2 }x }{ \sqrt { { tan }^{ 2 }x+4 } }$
Solution:

Ex 7.4 Class 12 Maths Question 10.
$\frac { 1 }{ \sqrt { { x }^{ 2 }+2x+2 } }$
Solution:

Ex 7.4 Class 12 Maths Question 11.

$\frac { 1 }{ { 9x }^{ 2 }+6x+5 }$
Solution:

Ex 7.4 Class 12 Maths Question 12.
$\frac { 1 }{ \sqrt { 7-6x-{ x }^{ 2 } } }$
Solution:
miscellaneous exercise on chapter 7 class 12 Q 12
Ex 7.4 Class 12 Maths Question 13.
$\frac { 1 }{ \sqrt { (x-1)(x-2) } }$
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.4 Q 13
Ex 7.4 Class 12 Maths Question 14.
$\frac { 1 }{ \sqrt { 8+3x-{ x }^{ 2 } } }$
Solution:
miscellaneous exercise on chapter 7 class 12 Q 14
Ex 7.4 Class 12 Maths Question 15.
$\frac { 1 }{ \sqrt { (x-a)(x-b) } }$
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.4 Q 15
Ex 7.4 Class 12 Maths Question 16.
$\frac { 4x+1 }{ \sqrt { { 2x }^{ 2 }+x-3 } }$
Solution:
Class 12 Maths Solutions Ex 7.4 Q 16
Ex 7.4 Class 12 Maths Question 17.
$\frac { x+2 }{ \sqrt { { x }^{ 2 }-1 } }$
Solution:

Ex 7.4 Class 12 Maths Question 18.
$\frac { 5x-2 }{ 1+2x+{ 3x }^{ 2 } }$
Solution:
put 5x-2=A $\frac { d }{ dx }$ (1+2x+3x²)+B
⇒ 6A=5, A= $\frac { 5 }{ 6 }-2=2A+B$ , B= $-\frac { 11 }{ 3 }$
NCERT Solutions for Class 12 Maths Chapter 7 Integrals 18

Ex 7.4 Class 12 Maths Question 19.
$\frac { 6x+7 }{ \sqrt { (x-5)(x-4) } }$
Solution:
Class 12 Maths Solutions Ex 7.4 Q 18

Ex 7.4 Class 12 Maths Question 20.
$\frac { x+2 }{ \sqrt { 4x-{ x }^{ 2 } } }$
Solution:

Ex 7.4 Class 12 Maths Question 21.
$\frac { x+2 }{ \sqrt { { x }^{ 2 }+2x+3 } }$
Solution:

Ex 7.4 Class 12 Maths Question 22.
$\frac { x+3 }{ { x }^{ 2 }-2x-5 }$
Solution:
NCERT Maths Class 12 Ex 7.4 Q 21

Ex 7.4 Class 12 Maths Question 23.
$\frac { 5x+3 }{ \sqrt { { x }^{ 2 }+4x+10 } }$
Solution:

Ex 7.4 Class 12 Maths Question 24.
$\int { \frac { dx }{ { x }^{ 2 }+2x+2 } equals }$
(a) xtan^-1(x+1)+c
(b) (x+1)tan^-1x+c
(c) tan^-1(x+1)+c
(d) tan^-1x+c
Solution:
NCERT Maths Class 12 Ex 7.4 Q 23
Ex 7.4 Class 12 Maths Question 25.
$\int { \frac { dx }{ \sqrt { 9x-{ 4x }^{ 2 } } } equals }$
(a) $\frac { 1 }{ 9 } { sin }^{ -1 }\left( \frac { 9x-8 }{ 8 } \right) +c$
(b) $\frac { 1 }{ 2 } { sin }^{ -1 }\left( \frac { 8x-9 }{ 9 } \right) +c$
(c) $\frac { 1 }{ 3 } { sin }^{ -1 }\left( \frac { 9x-8 }{ 8 } \right) +c$
(d) ${ sin }^{ -1 }\left( \frac { 9x-8 }{ 9 } \right) +c$
Solution:
NCERT Maths Class 12 Ex 7.4 Q 24

Move to Top → Class 12 Integrals Chapter 7

Integrals Class 12 Ex 7.5

Ex 7.5 Class 12 Maths Question 1.
$\frac { x }{ (x+1)(x+2) }$
Solution:
NCERT Solutions Maths Class 12 Ex 7.5 Q 1
Ex 7.5 Class 12 Maths Question 2.
$\frac { 1 }{ { x }^{ 2 }-9 }$
Solution:

Ex 7.5 Class 12 Maths Question 3.
$\frac { 3x-1 }{ (x-1)(x-2)(x-3) }$
Solution:

Ex 7.5 Class 12 Maths Question 4.
$\frac { x }{ (x-1)(x-2)(x-3) }$
Solution:

Ex 7.5 Class 12 Maths Question 5.
$\frac { 2x }{ { x }^{ 2 }+3x+2 }$
Solution:
Chapter 7 Class 12 Maths Ex 7.5 Q 5
Ex 7.5 Class 12 Maths Question 6.
$\frac { 1-{ x }^{ 2 } }{ x(1-2x) }$
Solution:

Ex 7.5 Class 12 Maths Question 7.
$\frac { x }{ \left( { x }^{ 2 }+1 \right) \left( x-1 \right) }$
Solution:

Ex 7.5 Class 12 Maths Question 8.
$\frac { x }{ { \left( x-1 \right) }^{ 2 }\left( x+2 \right) }$
Solution:
Class 12 Integration NCERT Solutions Ex 7.5 Q 8
Ex 7.5 Class 12 Maths Question 9.
$\frac { 3x+5 }{ { x }^{ 3 }-{ x }^{ 2 }-x+1 }$
Solution:

Ex 7.5 Class 12 Maths Question 10.
$\frac { 2x-3 }{ ({ x }^{ 2 }-1)(2x+3) }$
Solution:

Ex 7.5 Class 12 Maths Question 11.
$\frac { 5x }{ (x-1)({ x }^{ 2 }-4) }$
Solution:
Class 12 Integration NCERT Solutions Ex 7.5 Q 11
Ex 7.5 Class 12 Maths Question 12.
$\frac { { x }^{ 3 }+x+1 }{ { x }^{ 2 }-1 }$
Solution:

Ex 7.5 Class 12 Maths Question 13.
$\frac { 2 }{ (1-x)(1+{ x }^{ 2 }) }$
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 Miscellaneous Exercise Q 13
Ex 7.5 Class 12 Maths Question 14.
$\frac { 3x-1 }{ { (x+2) }^{ 2 } }$
Solution:

Ex 7.5 Class 12 Maths Question 15.
$\frac { 1 }{ { x }^{ 4 }-1 }$
Solution:

Ex 7.5 Class 12 Maths Question 16.
$\frac { 1 }{ x({ x }^{ n }+1) }$
[Hint : multiply numerator and denominator by x^n-1 and put xⁿ = t ]
Solution:
Class 12 Maths Ex 7.5 Q 16
Class 12 Maths Ex 7.5 Q 16 - i
Ex 7.5 Class 12 Maths Question 17.
$\frac { cosx }{ (1-sinx)(2-sinx) }$
Solution:
Class 12 Maths Ex 7.5 Q 17
Ex 7.5 Class 12 Maths Question 18.
$\frac { \left( { x }^{ 2 }+1 \right) \left( { x }^{ 2 }+2 \right) }{ \left( { x }^{ 2 }+3 \right) \left( { x }^{ 2 }+4 \right) }$
Solution:
Class 12 Maths Ex 7.5 Q 18
Class 12 Maths Ex 7.5 Q 18 - i
Ex 7.5 Class 12 Maths Question 19.
$\frac { 2x }{ ({ x }^{ 2 }+1)({ x }^{ 2 }+3) }$
Solution:
NCERT Class 12 Maths Ex 7.5 Q 19
Ex 7.5 Class 12 Maths Question 20.
$\frac { 1 }{ x({ x }^{ 4 }-1) }$
Solution:

Ex 7.5 Class 12 Maths Question 21.
$\frac { 1 }{ { e }^{ x }-1 }$
Solution:

Ex 7.5 Class 12 Maths Question 22.
choose the correct answer in each of the following :
$\int { \frac { xdx }{ (x-1)(x-2) } equals }$
(a) $log\left| \frac { { (x-1) }^{ 2 } }{ x-2 } \right| +c$
(b) $log\left| \frac { { (x-2) }^{ 2 } }{ x-1 } \right| +c$
(c) $log\left| \left( \frac { x-{ 1 }^{ 2 } }{ x-2 } \right) \right| +c$
(d) log|(x-1)(x-2)|+c
Solution:
NCERT Class 12 Maths Ex 7.5 Q 22
Ex 7.5 Class 12 Maths Question 23.
$\int { \frac { dx }{ x({ x }^{ 2 }+1) } equals }$
(a) $log|x|-\frac { 1 }{ 2 } log({ x }^{ 2 }+1)+c$
(b) $log|x|+\frac { 1 }{ 2 } log({ x }^{ 2 }+1)+c$
(c) $-log|x|+\frac { 1 }{ 2 } log({ x }^{ 2 }+1)+c$
(d) $\frac { 1 }{ 2 } log|x|+log({ x }^{ 2 }+1)+c$
Solution:
NCERT Class 12 Maths Ex 7.5 Q 23

Move to Top → Class 12 Integrals Chapter 7

Integrals Class 12 Ex 7.6

Ex 7.6 Class 12 Maths Question 1.
x sinx
Solution:
Maths Class 12 NCERT Solutions Chapter 7 Ex 7.6 Q 1
Ex 7.6 Class 12 Maths Question 2.
x sin3x
Solution:

Ex 7.6 Class 12 Maths Question 3.
${ x }^{ 2 }{ e }^{ x }$
Solution:

Ex 7.6 Class 12 Maths Question 4.
x logx
Solution:

Ex 7.6 Class 12 Maths Question 5.
x log2x
Solution:
NCERT Maths Solution Class 12 Ex 7.6 Q 5
Ex 7.6 Class 12 Maths Question 6.
${ x }^{ 2 }logx$
Solution:

Ex 7.6 Class 12 Maths Question 7.
$x\quad { sin }^{ -1 }x$
Solution:

Ex 7.6 Class 12 Maths Question 8.
$x\quad { tan }^{ -1 }x$
Solution:

Ex 7.6 Class 12 Maths Question 9.
$x\quad { cos }^{ -1 }x$
Solution:
Class 12 Maths NCERT Solution Ex 7.6 Q 9

Ex 7.6 Class 12 Maths Question 10.
${ (sin }^{ -1 }{ x })^{ 2 }$
Solution:

Ex 7.6 Class 12 Maths Question 11.
$\frac { x\quad { cos }^{ -1 }x }{ \sqrt { 1-{ x }^{ 2 } } }$
Solution:

Ex 7.6 Class 12 Maths Question 12.
x sec²x
Solution:
Class 12 Maths NCERT Solution Ex 7.6 Q 12
Ex 7.6 Class 12 Maths Question 13.
${ ta }n^{ -1 }x$
Solution:

Ex 7.6 Class 12 Maths Question 14.
x(logx)²
Solution:

Ex 7.6 Class 12 Maths Question 15.
(x²+1)logx
Solution:

Ex 7.6 Class 12 Maths Question 16.
${ e }^{ x }(sinx+cosx)$
Solution:
Class 12 Maths NCERT Solution Q 16
Ex 7.6 Class 12 Maths Question 17.
$\frac { { xe }^{ x } }{ { (1+x) }^{ 2 } }$
Solution:
Ch 7 Maths Class 12 Ex 7.6 Q 17
Ex 7.6 Class 12 Maths Question 18.
$\frac { { e }^{ x }(1+sinx) }{ 1+cosx }$
Solution:

Ex 7.6 Class 12 Maths Question 19.
${ e }^{ x }\left( \frac { 1 }{ x } -\frac { 1 }{ { x }^{ 2 } } \right)$
Solution:

Ex 7.6 Class 12 Maths Question 20.
$\frac { { (x-2)e }^{ x } }{ { (x-1) }^{ 3 } }$
Solution:
Ch 7 Maths Class 12 Ex 7.6 Q 20
Ex 7.6 Class 12 Maths Question 21.
${ e }^{ 2x }sinx$
Solution:

Ex 7.6 Class 12 Maths Question 22.
${ sin }^{ -1 }\left( \frac { 2x }{ 1+{ x }^{ 2 } } \right)$
Solution:
Maths Class 12 Chapter 7 NCERT Solutions Ex 7.6 Q 22

Choose the correct answer in exercise 23 and 24

Ex 7.6 Class 12 Maths Question 23.
$\int { { x }^{ 2 }{ e }^{ { x }^{ 3 } } } dx\quad equals$
(a) $\frac { 1 }{ 3 } { e }^{ { x }^{ 3 } }+c$
(b) $\frac { 1 }{ 3 } +{ e }^{ { x }^{ 2 } }+c$
(c) $\frac { 1 }{ 2 } { e }^{ { x }^{ 3 } }+c$
(d) $\frac { 1 }{ 2 } { e }^{ { x }^{ 2 } }+c$
Solution:
Maths Class 12 Chapter 7 NCERT Solutions Ex 7.6 Q 23
Ex 7.6 Class 12 Maths Question 24.
$\int { { e }^{ x }secx(1+tanx) } dx\quad equals$
(a) ${ e }^{ x }cosx+c$
(b) ${ e }^{ x }secx+c$
(c) ${ e }^{ x }sinx+c$
(d) ${ e }^{ x }tanx+c$
Solution:
NCERT Maths Solutions for Class 12 Ex 7.6 Q 24

Move to Top → Class 12 Integrals Chapter 7

Class 12 Integrals Ex 7.7

Integral the function in exercises 1 to 9

Ex 7.7 Class 12 Maths Question 1.
$\sqrt { 4-{ x }^{ 2 } }$
Solution:
Maths NCERT Class 12 Ex 7.7 Q 1
Ex 7.7 Class 12 Maths Question 2.
$\sqrt { 1-{ 4x }^{ 2 } }$
Solution:

Ex 7.7 Class 12 Maths Question 3.
$\sqrt { { x }^{ 2 }+4x+6 }$
Solution:

Ex 7.7 Class 12 Maths Question 4.
$\sqrt { { x }^{ 2 }+4x+1 }$
Solution:

Ex 7.7 Class 12 Maths Question 5.
$\sqrt { 1-4x-{ x }^{ 2 } }$
Solution:
Maths NCERT Class 12 Ex 7.7 Q 5
Ex 7.7 Class 12 Maths Question 6.
$\sqrt { { x }^{ 2 }+4x-5 }$
Solution:
NCERT Solutions Class 12 Ex 7.7 Q 6
Ex 7.7 Class 12 Maths Question 7.
$\sqrt { 1+3x-{ x }^{ 2 } }$
Solution:

Ex 7.7 Class 12 Maths Question 8.
$\sqrt { { x }^{ 2 }+3x }$
Solution:

Ex 7.7 Class 12 Maths Question 9.
$\sqrt { 1+\frac { { x }^{ 2 } }{ 9 } }$
Solution:

Choose the correct answer in the Exercises 10 to 11:

Ex 7.7 Class 12 Maths Question 10.
$\int { \sqrt { 1+{ x }^{ 2 } } } dx\quad is\quad equal\quad to$
(a) $\frac { x }{ 2 } \sqrt { 1+{ x }^{ 2 } } +\frac { 1 }{ 2 } log|x+\sqrt { 1+{ x }^{ 2 } } |+c$
(b) $\frac { 2 }{ 3 } { \left( 1+{ x }^{ 2 } \right) }^{ \frac { 3 }{ 2 } }+c$
(c) $\frac { 2 }{ 3 } x{ \left( 1+{ x }^{ 2 } \right) }^{ \frac { 3 }{ 2 } }+c$
(d) $\frac { { x }^{ 2 } }{ 2 } \sqrt { 1+{ x }^{ 2 } } +\frac { 1 }{ 2 } { x }^{ 2 }log\left| x+\sqrt { 1+{ x }^{ 2 } } \right| +c$
Solution:
Exercise 7.7 Class 12 Maths Q 10
Ex 7.7 Class 12 Maths Question 11.
$\int { \sqrt { { x }^{ 2 }-8x+7 } } dx\quad is\quad equal\quad to$
NCERT Solutions for Class 12 Maths Chapter 7 Integrals 11
Solution:

Move to Top → Class 12 Integrals Chapter 7

Class 12 Integrals Ex 7.8

Ex 7.8 Class 12 Maths Question 1.
$\int _{ a }^{ b }{ x\quad dx }$
Solution:
Maths NCERT Class 12 Ex 7.8 Q 1

Ex 7.8 Class 12 Maths Question 2.
$\int _{ 0 }^{ 5 }{ (x+1)dx }$
Solution:
Maths NCERT Class 12 Ex 7.8 Q 2

Ex 7.8 Class 12 Maths Question 3.
$\int _{ 2 }^{ 3 }{ { x }^{ 2 } } dx$
Solution:
Maths NCERT Class 12 Ex 7.8 Q 3

Ex 7.8 Class 12 Maths Question 4.
$\int _{ 1 }^{ 4 }{ ({ x }^{ 2 }-x) } dx$
Solution:
NCERT Solutions Class 12 Ex 7.8 Q 4

Ex 7.8 Class 12 Maths Question 5.
$\int _{ -1 }^{ 1 }{ { e }^{ x } } dx\quad$
Solution:
Maths NCERT Class 12 Ex 7.8 Q 5

Ex 7.8 Class 12 Maths Question 6.
$\int _{ 0 }^{ 4 }{ { (x+e }^{ 2x }) } dx\quad$
Solution:
Maths NCERT Class 12 Ex 7.8 Q 6

Move to Top → Class 12 Integrals Chapter 7

Class 12 Integrals Ex 7.9

Ex 7.9 Class 12 Maths Question 1.
$\int _{ -1 }^{ 1 }{ { (x+1 }) } dx\quad$
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 Ex 7.9 Q 1

Ex 7.9 Class 12 Maths Question 2.
$\int _{ 2 }^{ 3 }{ \frac { 1 }{ x } dx }$
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 Ex 7.9 Q 2

Ex 7.9 Class 12 Maths Question 3.
$\int _{ 1 }^{ 2 }{ \left( { 4x }^{ 3 }-{ 5x }^{ 2 }+6x+9 \right) dx }$
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 Ex 7.9 Q 3

Ex 7.9 Class 12 Maths Question 4.
$\int _{ 0 }^{ \frac { \pi }{ 4 } }{ sin2x\quad dx }$
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 Ex 7.9 Q 4

Ex 7.9 Class 12 Maths Question 5.
$\int _{ 0 }^{ \frac { \pi }{ 2 } }{ cos2x\quad dx }$
Solution:
NCERT Integration Ex 7.9 Q 5

Ex 7.9 Class 12 Maths Question 6.
$\int _{ 4 }^{ 5 }{ { e }^{ x }dx }$
Solution:
NCERT Integration Ex 7.9 Q 6

Ex 7.9 Class 12 Maths Question 7.
$\int _{ 0 }^{ \frac { \pi }{ 4 } }{ tanx\quad dx }$
Solution:
NCERT Integration Ex 7.9 Q 7

Ex 7.9 Class 12 Maths Question 8.
$\int _{ \frac { \pi }{ 6 } }^{ \frac { \pi }{ 4 } }{ cosec\quad xdx }$
Solution:
NCERT Integration Ex 7.9 Q 8

Ex 7.9 Class 12 Maths Question 9.
$\int _{ 0 }^{ 1 }{ \frac { dx }{ \sqrt { 1-{ x }^{ 2 } } } }$
Solution:
NCERT Class 12 Maths Solution Ex 7.9 Q 9

Ex 7.9 Class 12 Maths Question 10.
$\int _{ 0 }^{ 1 }{ \frac { dx }{ 1+{ x }^{ 2 } } }$
Solution:
NCERT Class 12 Maths Solution Ex 7.9 Q 10

Ex 7.9 Class 12 Maths Question 11.
$\int _{ 2 }^{ 3 }{ \frac { dx }{ { x }^{ 2 }-1 } }$
Solution:
NCERT Class 12 Maths Solution Ex 7.9 Q 11

Ex 7.9 Class 12 Maths Question 12.
$\int _{ 0 }^{ \frac { \pi }{ 2 } }{ { cos }^{ 2 } } xdx$
Solution:
NCERT Class 12 Maths Solution Ex 7.9 Q 12

Ex 7.9 Class 12 Maths Question 13.
$\int _{ 2 }^{ 3 }{ \frac { x }{ { x }^{ 2 }+1 } } dx$
Solution:
Ex 7.9 Class 12 Q 13

Ex 7.9 Class 12 Maths Question 14.
$\int _{ 0 }^{ 1 }{ \frac { 2x+3 }{ { 5x }^{ 2 }+1 } dx }$
Solution:
Ex 7.9 Class 12 Q 14

Ex 7.9 Class 12 Maths Question 15.
$\int _{ 0 }^{ 1 }{ { xe }^{ { x }^{ 2 } }dx }$
Solution:
Ex 7.9 Class 12 Q 15

Ex 7.9 Class 12 Maths Question 16.
$\int _{ 1 }^{ 2 }{ \frac { { 5x }^{ 2 } }{ { x }^{ 2 }+4x+3 } dx }$
Solution:
Ex 7.9 Class 12 Q 16
Ex 7.9 Class 12 Q 16 - i

Ex 7.9 Class 12 Maths Question 17.
$\int _{ 0 }^{ \frac { \pi }{ 4 } }{ \left( { 2sec }^{ 2 }x+{ x }^{ 3 }+2 \right) dx }$
Solution:
Ex 7.9 Class 12 Q 17

Ex 7.9 Class 12 Maths Question 18.
$\int _{ 0 }^{ \pi }{ \left( { sin }^{ 2 }\frac { x }{ 2 } -{ cos }^{ 2 }\frac { x }{ 2 } \right) } dx$
Solution:
Maths NCERT Class 12 Solutions Ex 7.9 Q 18

Ex 7.9 Class 12 Maths Question 19.
$\int _{ 0 }^{ 2 }{ \frac { 6x+3 }{ { x }^{ 2 }+4 } } dx$
Solution:
Maths NCERT Class 12 Solutions Ex 7.9 Q 19

Ex 7.9 Class 12 Maths Question 20.
$\int _{ 0 }^{ 1 }{ \left( { xe }^{ x }+sin\frac { \pi x }{ 4 } \right) dx }$
Solution:
Maths NCERT Class 12 Solutions Ex 7.9 Q 20

Ex 7.9 Class 12 Maths Question 21.
$\int _{ 1 }^{ \sqrt { 3 } }{ \frac { dx }{ { 1+x }^{ 2 } } \quad equals }$
(a) $\frac { \pi }{ 3 }$
(b) $\frac { 2\pi }{ 3 }$
(c) $\frac { \pi }{ 6 }$
(d) $\frac { \pi }{ 12 }$
Solution:
Maths NCERT Class 12 Solutions Ex 7.9 Q 21

Ex 7.9 Class 12 Maths Question 22.
$\int _{ 0 }^{ \frac { 2 }{ 3 } }{ \frac { dx }{ 4+{ 9x }^{ 2 } } equals }$
(a) $\frac { \pi }{ 6 }$
(b) $\frac { \pi }{ 12 }$
(c) $\frac { \pi }{ 24 }$
(d) $\frac { \pi }{ 4 }$
Solution:
Maths NCERT Class 12 Solutions Ex 7.9 Q 22

Move to Top → Class 12 Integrals Chapter 7

Integration Class 12 Ex 7.10

Ex 7.10 Class 12 Maths Question 1:
Ex 7.10 Integrals Class 12 NCERT Solutions Ex 7.10 Q 1
Solution:
NCERT Solutions of Class 12 Maths Chapter 7 Integrals Ex 7.10 Q 1
Ex 7.10 Class 12 Maths Question 2:

Solution:

Ex 7.10 Class 12 Maths Question 3:

Solution:

Ex 7.10 Class 12 Maths Question 4:
Integration Class 12 Ex 7.10 Q 4
Solution:

Ex 7.10 Class 12 Maths Question 5:

Solution:
NCERT Solutions of Class 12 Maths Chapter 7 Integrals Ex 7.10 Q 5

Ex 7.10 Class 12 Maths Question 6:

Solution:
NCERT Class 12 Solutions Integrals Ex 7.10 Q 6

Ex 7.10 Class 12 Maths Question 7:

Solution:

Ex 7.10 Class 12 Maths Question 8:

Solution:

Ex 7.10 Class 12 Maths Question 9:
Integration Class 12 Ex 7.10 Q 9
Solution:
ncert solution of maths class 12 Chapter 7 Ex 7.10 Q 9
Ex 7.10 Class 12 Maths Question 10:

Solution:

Ex 7.10 Class 12 Maths Question 11:
Integrals Class 12 Ex 7.10 11
Solution:

Ex 7.10 Class 12 Maths Question 12:

Solution:
NCERT Class 12 Solutions Ex 7.10 Q 12

Ex 7.10 Class 12 Maths Question 13:

Solution:

Ex 7.10 Class 12 Maths Question 14:
integrals class 12 ncert solutions Ex 7.10 Q 14
Solution:

Ex 7.10 Class 12 Maths Question 15:

Solution:

Ex 7.10 Class 12 Maths Question 16:
maths ncert solutions class 12 Ex 7.10 Q 16
Solution:
NCERT Maths 12 Solutions Ex 7.10 Q 16
Ex 7.10 Class 12 Maths Question 17:

Solution:

Ex 7.10 Class 12 Maths Question 18:

Solution:

Ex 7.10 Class 12 Maths Question 19:

Solution:

Ex 7.10 Class 12 Maths Question 20:

maths ncert solutions class 12 Ex 7.10 Q 20 - i
Solution:
NCERT Maths 12 Solutions Ex 7.10 Q 20

Move to Top → Class 12 Integrals Chapter 7

NCERT Solutions for Class 2 Maths Integration Class 12 Ex 7.11

Ex 7.11 Integrals Class 12 Maths NCERT Solutions Sol 1

integrals ncert solutions Ex 7.11 Q 5

Ex 7.11 Integration Class 12 Maths NCERT Solutions Sol 6

NCERT maths solutions class 12 Ex 7.11 Sol 11

NCERT solutions for class 12 maths Ex 7.11 Sol 16

integration class 12 ncert solutions Ex 7.11 Q 20

Maths NCERT Solution Class 12 Ex 7.11 Q 26

Move to Top → Class 12 Integrals Chapter 7

NCERT Solutions for Class 12 Maths Chapter 7 Integrals Miscellaneous Exercise

Miscellaneous Exercise Class 11 Maths Question 1:

Solution:
ncert solutions class 12 maths Miscellaneous Questions Q 1 - i

Miscellaneous Exercise Class 11 Maths Question 2:
ncert solutions class 12 maths Miscellaneous Questions Q 2
Solution:

Miscellaneous Exercise Class 11 Maths Question 3:

Solution:
ncert solutions class 12 maths Miscellaneous Questions Q 3 - i

vMiscellaneous Exercise Class 11 Maths Question 4:
ncert solutions class 12 maths Miscellaneous Questions Q 4
Solution:
miscellaneous exercise on chapter 7 class 12 Q 4 - i

Miscellaneous Exercise Class 11 Maths Question 5:
ncert solutions class 12 maths Miscellaneous Questions Q 5
Solution:

Miscellaneous Exercise Class 11 Maths Question 6:

Solution:
ncert solutions class 12 maths Miscellaneous Questions Q 6 - i

Miscellaneous Exercise Class 11 Maths Question 7:
ncert solutions class 12 maths Miscellaneous Question Q 7
Solution:

Miscellaneous Exercise Class 11 Maths Question 8:

Solution:
ncert solutions class 12 maths Miscellaneous Questions Q 8 - i

Miscellaneous Exercise Class 11 Maths Question 9:

Solution:
ncert solutions for class 12 maths miscellaneous Q 9 - i

Miscellaneous Exercise Class 11 Maths Question 10:
ncert solutions class 12 maths Miscellaneous Questions Q 10
Solution:

Miscellaneous Exercise Class 11 Maths Question 11:

Solution:

Miscellaneous Exercise Class 11 Maths Question 12:

Solution:
ncert miscellaneous solutions class 12 Q 12 - i

Miscellaneous Exercise Class 11 Maths Question 13:

Solution:
ncert solutions class 12 maths Miscellaneous Questions Q 13 - i

Miscellaneous Exercise Class 11 Maths Question 14:
ncert solutions class 12 maths Miscellaneous Questions Q 14
Solution:
ncert solutions for class 12 maths chapter 7 miscellaneous Q 14

Miscellaneous Exercise Class 11 Maths Question 15:

Solution:
ncert solutions class 12 maths Miscellaneous Questions Q 15 - i

Miscellaneous Exercise Class 11 Maths Question 16:

Solution:
ncert solutions class 12 maths Miscellaneous Questions Q 16 - i

Miscellaneous Exercise Class 11 Maths Question 17:
ncert solutions class 12 maths Miscellaneous Questions Q 17
Solution:

Miscellaneous Exercise Class 11 Maths Question 18:
ncert solutions class 12 maths Miscellaneous Questions Q 18
Solution:

Miscellaneous Exercise Class 11 Maths Question 20:
ncert solutions class 12 maths Miscellaneous Questions Q 20
Solution:

Miscellaneous Exercise Class 11 Maths Question 21:
ncert solutions class 12 maths Miscellaneous Questions Q 21
Solution:

Miscellaneous Exercise Class 11 Maths Question 22:

Solution:
ncert solutions class 12 maths Miscellaneous Questions Q 22 - i

Miscellaneous Exercise Class 11 Maths Question 23:
ncert solutions class 12 maths Miscellaneous Questions Q 23
Solution:

Miscellaneous Exercise Class 11 Maths Question 24:
ncert solutions class 12 maths Miscellaneous Questions Q 24
Solution:

ncert miscellaneous solutions class 12 Q 24 - ii

Miscellaneous Exercise Class 11 Maths Question 25:
ncert solutions class 12 maths Miscellaneous Questions Q 25
Solution:

Miscellaneous Exercise Class 11 Maths Question 26:
ncert solutions class 12 maths Miscellaneous Questions Q 26
Solution:

Miscellaneous Exercise Class 11 Maths Question 27:
maths class 12 ncert solutions miscellaneous exercise 27
Solution:

Miscellaneous Exercise Class 11 Maths Question 28:
maths class 12 ncert solutions miscellaneous exercise 28
Solution:

Miscellaneous Exercise Class 11 Maths Question 29:
maths class 12 ncert solutions miscellaneous exercise 29
Solution:

Miscellaneous Exercise Class 11 Maths Question 30:
maths class 12 ncert solutions miscellaneous exercise 30

Miscellaneous Exercise Class 11 Maths Question 31:

Solution:
maths class 12 ncert solutions miscellaneous exercise 31 - i

Miscellaneous Exercise Class 11 Maths Question 32:

Solution:
maths class 12 ncert solutions miscellaneous exercise 32- i

Miscellaneous Exercise Class 11 Maths Question 33:

Solution:

Integration Class 12 NCERT Solutions Miscellaneous Exercise Q 33 - ii

Miscellaneous Exercise Class 11 Maths Question 34:
Integration Class 12 NCERT Solutions Miscellaneous Exercise Q 34
Solution:

Question 35:

Solution:
Integration Class 12 NCERT Solutions Miscellaneous Exercise Q 35 -i

Miscellaneous Exercise Class 11 Maths Question 36:

Solution:
Integration Class 12 NCERT Solutions Miscellaneous Exercise Q 36 -i

Miscellaneous Exercise Class 11 Maths Question 37:
Integration Class 12 NCERT Solutions Miscellaneous Exercise Q 37
Solution:

Miscellaneous Exercise Class 11 Maths Question 38:

Solution:
Integration Class 12 NCERT Solutions Miscellaneous Exercise Q 38 -i

Miscellaneous Exercise Class 11 Maths Question 39:

Solution:
Integration Class 12 NCERT Solutions Miscellaneous Exercise Q 39-i

Miscellaneous Exercise Class 11 Maths Question 40:

Solution:
Integration Class 12 NCERT Solutions Miscellaneous Exercise Q 40 -i

Miscellaneous Exercise Class 11 Maths Question 41:

Solution:
Integration Class 12 NCERT Solutions Miscellaneous Exercise Q 41 -i

Miscellaneous Exercise Class 11 Maths Question 42:
Integration Class 12 NCERT Solutions Miscellaneous Exercise Q 42
Solution:

Miscellaneous Exercise Class 11 Maths Question 43:

Solution:
Integration Class 12 NCERT Solutions Miscellaneous Exercise Q 43-i

Miscellaneous Exercise Class 11 Maths Question 44:
Integration Class 12 NCERT Solutions Miscellaneous Exercise Q 44
Solution:

Move to Top → Class 12 Integrals Chapter 7

Integration Formulas

integration formulas

integration formulas pdf
integration formulae
formulas of integration
basic integration formulas
integration formulas pdf for class 12

Move to Top → Class 12 Integrals Chapter 7

गणित कक्षा 12 समाकलन प्रश्नावली 7.1

निम्नलिखित फलनों के प्रतिअवकलज ( समाकलन) निरीक्षण विधि द्वारा ज्ञात कीजिए।

Ex 7.1 Class 11 Maths प्रश्न 1.
sin 2x
हल-
∫sin 2x dx
हम जानते हैं कि, $\frac { d }{ dx }$ cos2x = -2 sin 2x
गणित एनसीईआरटी हल कक्षा 12 समाकलन प्रश्नावली 7.1 1

Ex 7.1 Class 11 Maths प्रश्न 2.
cos 3x
हल-
∫cos 3x dx
हम जानते हैं कि, $\frac { d }{ dx }$ sin 3x = 3 cos 3x
गणित एनसीईआरटी हल कक्षा 12 समाकलन प्रश्नावली 7.1 2

Ex 7.1 Class 11 Maths प्रश्न 3.
e^2x
हल-
∫e^2x dx
हम जानते हैं कि,
गणित एनसीईआरटी हल कक्षा 12 समाकलन प्रश्नावली 7.1 3

Ex 7.1 Class 11 Maths प्रश्न 4.
(ax + b)²
हल-
∫(ax + b)² dx
हम जानते हैं कि,
गणित एनसीईआरटी हल कक्षा 12 समाकलन प्रश्नावली 7.1 4

Ex 7.1 Class 11 Maths प्रश्न 5.
sin 2x – 4e^3x
हल-
∫(sin 2x -4e^3x) dx = ∫sin 2x dx – 4∫e^3x …(1)
गणित एनसीईआरटी हल कक्षा 12 समाकलन प्रश्नावली 7.1 5

निम्नलिखित समाकलनों को ज्ञात कीजिए।

Ex 7.1 Class 11 Maths प्रश्न 6.
∫(4e^3x + 1) dx
हल-
∫(4e^3x + 1) dx = 4∫e^3xdx + ∫1 dx
गणित एनसीईआरटी हल कक्षा 12 समाकलन प्रश्नावली 7.1 6

Ex 7.1 Class 11 Maths प्रश्न 7.
गणित एनसीईआरटी हल कक्षा 12 समाकलन प्रश्नावली 7.1 7
हल-

Ex 7.1 Class 11 Maths प्रश्न 8.
∫(ax² + bx + c) dx
हल-
∫(ax² + bx + c) dx = a∫x²dx + b∫xdx + c∫1 dx
गणित एनसीईआरटी हल कक्षा 12 समाकलन प्रश्नावली 7.1 8

Ex 7.1 Class 11 Maths प्रश्न 9.
∫(2x² + e^x) dx
हल-
∫(2x² + e^x) dx = 2∫x² dx + ∫e^x dx
गणित एनसीईआरटी हल कक्षा 12 समाकलन प्रश्नावली 7.1 9

Ex 7.1 Class 11 Maths प्रश्न 10.
गणित एनसीईआरटी हल कक्षा 12 समाकलन प्रश्नावली 7.1 10
हल-

Ex 7.1 Class 11 Maths प्रश्न 11.
एनसीईआरटी हल कक्षा 12 गणित समाकलन प्रश्नावली 7.1 11
हल-

Ex 7.1 Class 11 Maths प्रश्न 12.
एनसीईआरटी हल कक्षा 12 गणित समाकलन प्रश्नावली 7.1 12
हल-

Ex 7.1 Class 11 Maths प्रश्न 13.
एनसीईआरटी हल कक्षा 12 गणित समाकलन प्रश्नावली 7.1 13
हल-

Ex 7.1 Class 11 Maths प्रश्न 14.
∫(1-x)√x dx
हल-
∫(1-x)√x dx
=∫(√x-x√x)dx
एनसीईआरटी हल कक्षा 12 गणित समाकलन प्रश्नावली 7.1 14

Ex 7.1 Class 11 Maths प्रश्न 15.
∫√x(3x² + 2x + 3)dx
हल-
∫√x(3x² + 2x + 3)dx
एनसीईआरटी हल कक्षा 12 गणित समाकलन प्रश्नावली 7.1 15

Ex 7.1 Class 11 Maths प्रश्न 16.
∫(2x – 3cosx + e^x)dx
हल-
∫(2x – 3cosx + e^x)dx
एनसीईआरटी हल कक्षा 12 गणित समाकलन प्रश्नावली 7.1 16

प्रश्न 17.
∫(2x² – 3sinx + 5√x)dx
हल-
∫(2x² – 3sinx + 5√x)dx
= 2∫x² dx – 3 ∫ sinx dx + 5∫√x dx
एनसीईआरटी हल कक्षा 12 गणित समाकलन प्रश्नावली 7.1 17

Ex 7.1 Class 11 Maths प्रश्न 18.
∫secx (sec x + tan x) dx
हल-
∫sec x (sec x + tan x) dx
= ∫(sec² x + sec x tan x) dx
= ∫(sec² x dx
= ∫sec x tan x dx
tan x + sec x + C

Ex 7.1 Class 11 Maths प्रश्न 19.
एनसीईआरटी हल कक्षा 12 गणित समाकलन प्रश्नावली 7.1 19
हल-

Ex 7.1 Class 11 Maths प्रश्न 20.

हल-
एनसीईआरटी हल कक्षा 12 गणित समाकलन प्रश्नावली 7.1 20.1

प्रश्न 21 एवं 22 में सही उत्तर का चयन कीजिए

Ex 7.1 Class 11 Maths प्रश्न 21
UP Board Solutions for Class 12 Maths Chapter 7 Integrals 21
हल-

Ex 7.1 Class 11 Maths प्रश्न 22
UP Board Solutions for Class 12 Maths Chapter 7 Integrals 22
हल-