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.

Free download NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.2 Integrals PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCERT Books based on updated CBSE Syllabus for the session 2019-20.

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:

Question 3.
$\frac { 1 }{ x+xlogx }$
Solution:

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:

Question 7.
$x\sqrt { x+2 }$
Solution:

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:

Question 11.
$\frac { x }{ \sqrt { x+4 } } ,x>0$
Solution:

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:

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

Question 15.
$\frac { x }{ 9-4{ x }^{ 2 } }$
Solution:

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:

Question 18.
$\frac { { e }^{ { tan }^{ -1 }x } }{ 1+{ x }^{ 2 } }$
Solution:

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:

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:

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:

Question 26.
$\frac { cos\sqrt { x } }{ \sqrt { x } }$
Solution:

Question 27.
$\sqrt { sin2x } cos2x$
Solution:

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:

Question 30.
$\frac { sinx }{ 1+cosx }$
Solution:

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:

Question 33.
$\frac { 1 }{ 1-tanx }$
Solution:

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

Question 36.
$\frac { (x+1){ (x+logx) }^{ 2 } }{ x }$
Solution:

Question 37.
$\frac { { x }^{ 3 }sin({ tan }^{ -1 }{ x }^{ 4 }) }{ 1+{ x }^{ 8 } } dx$
Solution:

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

गणित कक्षा 12 समाकलन प्रश्नावली 7.2

प्रश्न 1 से 37 तक के प्रश्नों में प्रत्येक फलने का समाकलन ज्ञात कीजिए

प्रश्न 1.
गणित एनसीईआरटी हल कक्षा 12 समाकलन प्रश्नावली 7.2 1
हल-

प्रश्न 2.
गणित एनसीईआरटी हल कक्षा 12 समाकलन प्रश्नावली 7.2 2
हल-

प्रश्न 3.
गणित एनसीईआरटी हल कक्षा 12 समाकलन प्रश्नावली 7.2 3
हल-

प्रश्न 4.
sin x sin (cos x)
हल-
मानी I = ∫ sin x sin (cos x) dx …(1)
माना cos x = t, दोनों पक्षों का x के सापेक्ष अवकलन करने पर,
– sin x dx = dt ⇒ sin x dx = – dt
∴(1) से, I = ∫sin (cos x) (sin x) dx = -∫sint dt
= cos t + C = cos (cos x) + C

प्रश्न 5.
sin (ax + b) cos (ax + b)
हल-
माना I = ∫sin (ax + b) cos (ax + b) dx
माना sin (ax + b) = t, दोनों पक्षों का x के सापेक्ष अवकलन करने पर,
a cos (ax + b) dx = dt
गणित एनसीईआरटी हल कक्षा 12 समाकलन प्रश्नावली 7.2 5

प्रश्न 6.
गणित एनसीईआरटी हल कक्षा 12 समाकलन प्रश्नावली 7.2 6
हल-
integration ncert solutions 6.1

प्रश्न 7.
ex 7.2 class 12
हल-
NCERT Solutions for Class 12 Maths Chapter 7 Integrals 7.1

प्रश्न 8.
integrals class 12 ncert solutions pdf
हल-
integration questions for class 12 pdf
integration full chapter pdf

प्रश्न 9.
integrals solutions
हल-
integration ncert

प्रश्न 10.
class 12 integration
हल-
integrals class 12 important questions

प्रश्न 11.
definite integral problems and solutions
हल-
NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.2

प्रश्न 12.
(x³ – 1)^1/3 x⁵
हल-
NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.2 in PDF

प्रश्न 13.
12 Maths ex. 7.2
हल-
integration 7.2

प्रश्न 14
12 maths Exercise 7.2 integration
हल-
12 maths chpater 7 ex. 7.2

प्रश्न 15
exercise 7.2 class 12
हल-
integrals 7.2

प्रश्न 16.
e^2x+3
हल-
7.2 for 12 maths

प्रश्न 17.
NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.2 for up board
हल-

प्रश्न 18.
NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.2 for mp board
हल-

प्रश्न 19.
12 Maths Chapter 7
हल-
Exercise 7.2 all questions

प्रश्न 20.
12 Maths 7.2
हल-
7.2 of 12 Maths

प्रश्न 21.
tan²(2x – 3)
हल-
Class 12 xercise 7.2 solutions

प्रश्न 22.
sec²(7 – 4x)
हल-
माना
I = ∫sec²(7 – 4x) …(1)
माना 7 – 4x = t, दोनों पक्षों का x के सापेक्ष अवकलन करने पर,
NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.2 guide free