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NCERT Solutions Class 12 Maths Chapter 7 – Download PDF

Get here NCERT Solutions Class 12 Maths Chapter 7. These NCERT Solutions for Class 12 of Maths subject includes detailed answers of all the questions in Chapter 7 – Integrals provided in NCERT Book which is prescribed for class 12 in schools.

Book: National Council of Educational Research and Training (NCERT)
Class: 12th Class
Subject: Maths
Chapter: Chapter 7 – Integrals

NCERT Solutions Class 12 Maths Chapter 7 – Free Download PDF

NCERT Solutions Class 12 Maths Chapter 7 – Integrals

NCERT Solutions for Class 12 Maths Chapter 7 – Integrals contains step-by-step and detailed solutions for every question.

Introduction
Integration as an Inverse Process of Differentiation
Geometrical interpretation of indefinite integral
Some properties of indefinite integral
Comparison between differentiation and integration
Methods of Integration
Integration by substitution
Integration using trigonometric identities
Integrals of Some Particular Functions
Integration by Partial Fractions
Integration by Parts
Integral of the type
Integrals of some more types
Definite Integral
Definite integral as the limit of a sum
Fundamental Theorem of Calculus
Area function
First fundamental theorem of integral calculus
Second fundamental theorem of integral calculus
Evaluation of Definite Integrals by Substitution
Some Properties of Definite Integrals

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

Question 3.
${ e }^{ 2x }$
Solution:

Question 4.
(ax + c)²
Solution:

Question 5.
${ sin\quad 2x-4e }^{ 3x }$
Solution:

Find the following integrals in Exercises 6 to 20 :

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

Question 8.
$\int { { (ax }^{ 2 }+bx+c)dx }$
Solution:

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

Question 11.
$\int { \frac { { x }^{ 3 }+{ 5x }^{ 2 }-4 }{ { x }^{ 2 } } dx }$
Solution:

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

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

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

Question 18.
$\int { secx(secx+tanx)dx }$
Solution:

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

Choose the correct answer in Exercises 21 and 22.
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
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