NCERT Solutions for Class 12 Maths Chapter 7 Integers Ex 7.4

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NCERT Solutions for Class 12 Maths Chapter 7 Integers Ex 7.4

Get Free NCERT Solutions for Class 12 Maths Chapter 7 Integers Ex 7.4 PDF. Integration Class 12 Maths NCERT Solutions are extremely helpful while doing your homework. Exercise 7.4 Class 12 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the questions in Chapter 7 Maths Class 12 Integrals Exercise 7.4 provided in NCERT Textbook.

The topics and sub-topics included in the Integrals chapter are the following:

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

 

NCERT Solutions for Class 12 Maths Chapter 7 Integers Ex 7.4

NCERT Solutions for Class 12 Maths Chapter 7 Integers Ex 7.4 are part of NCERT Solutions for Class 12 Maths. Here we have given Class 12 Maths NCERT Solutions Integrals Ex 7.4
Question 1.
\frac { { 3x }^{ 2 } }{ { x }^{ 6 }+1 }
Solution:
Class 12 Integrals NCERT Solutions Ex 7.4 Q 1
Question 2.
\frac { 1 }{ \sqrt { 1+{ 4x }^{ 2 } } }
Solution:
Class 12 Integrals NCERT Solutions Ex 7.4 Q 2
Question 3.
\frac { 1 }{ \sqrt { { (2-x) }^{ 2 }+1 } }
Solution:
Class 12 Integrals NCERT Solutions Ex 7.4 Q 3
Question 4.
\frac { 1 }{ \sqrt { 9-{ 25x }^{ 2 } } }
Solution:
Class 12 Integrals NCERT Solutions Ex 7.4 Q 4
Question 5.
\frac { 3x }{ 1+{ 2x }^{ 4 } }
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 PDF Ex 7.4 Q 5
Question 6.
\frac { { x }^{ 2 } }{ 1-{ x }^{ 6 } }
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 PDF Ex 7.4 Q 6
Question 7.
\frac { x-1 }{ \sqrt { { x }^{ 2 }-1 } }
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 PDF Ex 7.4 Q 7
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
Question 9.
\frac { { sec }^{ 2 }x }{ \sqrt { { tan }^{ 2 }x+4 } }
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.4 Q 9
Question 10.
\frac { 1 }{ \sqrt { { x }^{ 2 }+2x+2 } }
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.4 Q 10
Question 11.
\frac { 1 }{ { 9x }^{ 2 }+6x+5 }
Solution:
miscellaneous exercise on chapter 7 class 12 Q 11
Question 12.
\frac { 1 }{ \sqrt { 7-6x-{ x }^{ 2 } } }
Solution:
miscellaneous exercise on chapter 7 class 12 Q 12
Question 13.
\frac { 1 }{ \sqrt { (x-1)(x-2) } }
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.4 Q 13
Question 14.
\frac { 1 }{ \sqrt { 8+3x-{ x }^{ 2 } } }
Solution:
miscellaneous exercise on chapter 7 class 12 Q 14
Question 15.
\frac { 1 }{ \sqrt { (x-a)(x-b) } }
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.4 Q 15
Question 16.
\frac { 4x+1 }{ \sqrt { { 2x }^{ 2 }+x-3 } }
Solution:
Class 12 Maths Solutions Ex 7.4 Q 16
Question 17.
\frac { x+2 }{ \sqrt { { x }^{ 2 }-1 } }
Solution:
Class 12 Maths Solutions Ex 7.4 Q 17
Class 12 Maths Solutions Ex 7.4 Q 17 - i
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

Question 19.
\frac { 6x+7 }{ \sqrt { (x-5)(x-4) } }
Solution:
Class 12 Maths Solutions Ex 7.4 Q 18
Class 12 Maths Solutions Ex 7.4 Q 18 - i
Class 12 Maths Solutions Ex 7.4 Q 18 - ii
Question 20.
\frac { x+2 }{ \sqrt { 4x-{ x }^{ 2 } } }
Solution:
Class 12 Maths Solutions Ex 7.4 Q 19
Class 12 Maths Solutions Ex 7.4 Q 19 - i
Class 12 Maths Solutions Ex 7.4 Q 19 - ii
Question 21.
\frac { x+2 }{ \sqrt { { x }^{ 2 }+2x+3 } }
Solution:
Class 12 Maths Solutions Ex 7.4 Q 20
Class 12 Maths Solutions Ex 7.4 Q 20 - i
Question 22.
\frac { x+3 }{ { x }^{ 2 }-2x-5 }
Solution:
NCERT Maths Class 12 Ex 7.4 Q 21
NCERT Maths Class 12 Ex 7.4 Q 21 -i
Question 23.
\frac { 5x+3 }{ \sqrt { { x }^{ 2 }+4x+10 } }
Solution:
NCERT Maths Class 12 Ex 7.4 Q 22
NCERT Maths Class 12 Ex 7.4 Q 22 - i
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
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

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