NCERT Solutions for Class 12 Maths Chapter 7 Integers Ex 7.2

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NCERT Solutions for Class 12 Maths Chapter 7 Integers Ex 7.2

Get Free NCERT Solutions for Class 12 Maths Chapter 7 Integers Ex 7.2 PDF. Integration Class 12 Maths NCERT Solutions are extremely helpful while doing your homework. Exercise 7.2 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 7.2 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 7.2

NCERT Solutions for Class 12 Maths Chapter 7 Integers Ex 7.2 are part of NCERT Solutions for Class 12 Maths. Here we have given Class 12 Maths NCERT Solutions Integrals Ex 7.2

Integrate the functions in Exercises 1 to 37:

Question 1.
\frac { 2x }{ 1+{ x }^{ 2 } }
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.2 Q 1
Question 2.
\frac { { \left( logx \right) }^{ 2 } }{ x }
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.2 Q 2
Question 3.
\frac { 1 }{ x+xlogx }
Solution:
NCERT Solutions for Class 12 Maths Chapter 7 Integrals Ex 7.2 Q 3
Question 4.
sinx sin(cosx)
Solution:
ncert solutions class 12 maths Chapter 7 Integrals Ex 7.2 Q 4
Question 5.
sin(ax+b) cos(ax+b)
Solution:
class 12 integration NCERT Solutions Chapter 7 Ex 7.2 Q 5
Question 6.
\sqrt { ax+b }
Solution:
class 12 integration NCERT Solutions Chapter 7 Ex 7.2 Q 6
Question 7.
x\sqrt { x+2 }
Solution:
class 12 integration NCERT Solutions Chapter 7 Ex 7.2 Q 7
Question 8.
x\sqrt { 1+{ 2x }^{ 2 } }
Solution:
class 12 maths integration NCERT Solutions Chapter 7 Ex 7.2 Q 8

Question 9.
(4x+2)\sqrt { { x }^{ 2 }+x+1 }
Solution:
class 12 maths integration NCERT Solutions Chapter 7 Ex 7.2 Q 9
Question 10.
\frac { 1 }{ x-\sqrt { x } }
Solution:
class 12 maths integration NCERT Solutions Chapter 7 Ex 7.2 Q 10
Question 11.
\frac { x }{ \sqrt { x+4 } } ,x>0
Solution:
class 12 maths integration NCERT Solutions Chapter 7 Ex 7.2 Q 11
Question 12.
{ { (x }^{ 3 }-1) }^{ \frac { 1 }{ 3 } }.{ x }^{ 5 }
Solution:
ncert class 12 maths solutions Integrals Ex 7.2 Q 12
Question 13.
\frac { { x }^{ 2 } }{ { { (2+3x }^{ 3 }) }^{ 3 } }
Solution:
ncert class 12 maths solutions Integrals Ex 7.2 Q 13
Question 14.
\frac { 1 }{ x(logx)^{ m } } ,x>0
Solution:
ncert class 12 maths solutions Integrals Ex 7.2 Q 14
Question 15.
\frac { x }{ 9-4{ x }^{ 2 } }
Solution:
ncert class 12 maths solutions Integrals Ex 7.2 Q 14
Question 16.
{ e }^{ 2x+3 }
Solution:
ncert maths solutions class 12 Integration Chapter 7 Ex 7.2 Q 16
Question 17.
\frac { x }{ { e }^{ { x }^{ 2 } } }
Solution:
ncert maths solutions class 12 Integration Chapter 7 Ex 7.2 Q 17
Question 18.
\frac { { e }^{ { tan }^{ -1 }x } }{ 1+{ x }^{ 2 } }
Solution:
ncert maths solutions class 12 Integration Chapter 7 Ex 7.2 Q 18
Question 19.
\frac { { e }^{ 2x }-1 }{ { e }^{ 2x }+1 }
Solution:
integration ncert solutions Class 12 chapter 7 Ex 7.2 Q 19
Question 20.
\frac { { e }^{ 2x }-{ e }^{ 2x } }{ { e }^{ 2x }+{ e }^{ -2x } }
Solution:
integration ncert solutions Class 12 chapter 7 Ex 7.2 Q 20
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
Question 22.
sec²(7-4x)
Solution:
maths class 12 ncert solutions Chapter 7 Integration Ex 7.2 Q 22
Question 23.
\frac { { sin }^{ -1 }x }{ \sqrt { 1-{ x }^{ 2 } } }
Solution:
maths class 12 ncert solutions Chapter 7 Integration Ex 7.2 Q 23
Question 24.
\frac { 2cosx-3sinx }{ 6cosx+4sinx }
Solution:
Ex 7.2 class 12 maths NCERT Solutions Q 24
Question 25.
\frac { 1 }{ { cos }^{ 2 }x{ (1-tanx) }^{ 2 } }
Solution:
Ex 7.2 class 12 maths NCERT Solutions Q 25
Question 26.
\frac { cos\sqrt { x } }{ \sqrt { x } }
Solution:
Ex 7.2 class 12 maths NCERT Solutions Q 26
Question 27.
\sqrt { sin2x } cos2x
Solution:
Ex 7.2 class 12 maths NCERT Solutions Q 27
Question 28.
\frac { cosx }{ \sqrt { 1+sinx } }
Solution:
Integration Solutions class 12 Maths Chapter 7 Ex 7.2 Q 28
Question 29.
cotx log sinx
Solution:
Integration Solutions class 12 Maths Chapter 7 Ex 7.2 Q 29
Question 30.
\frac { sinx }{ 1+cosx }
Solution:
Integration Solutions class 12 Maths Chapter 7 Ex 7.2 Q 30
Question 31.
\frac { sinx }{ { (1+cosx) }^{ 2 } }
Solution:
NCERT Maths Class 12 Solutions Chapter 7 Ex 7.2 Q 31
Question 32.
\frac { 1 }{ 1+cotx }
Solution:
NCERT Maths Class 12 Solutions Chapter 7 Ex 7.2 Q 32
Question 33.
\frac { 1 }{ 1-tanx }
Solution:
NCERT Maths Class 12 Solutions Chapter 7 Ex 7.2 Q 33
Question 34.
\frac { \sqrt { tanx } }{ sinxcosx }
Solution:
NCERT Integration Solutions Ex 7.2 Q 34
Question 35.
\frac { { (1+logx) }^{ 2 } }{ x }
Solution:
NCERT Integration Solutions Ex 7.2 Q 35
Question 36.
\frac { (x+1){ (x+logx) }^{ 2 } }{ x }
Solution:
NCERT Integration Solutions Ex 7.2 Q 36
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

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
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

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