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

• Integration Formulas
• Integrals Class 12 Ex 7.1
• Integrals Class 12 Ex 7.1 in Hindi Medium
• Integrals Class 12 Ex 7.2
• Integrals Class 12 Ex 7.2 in Hindi Medium
• Integrals Class 12 Ex 7.3
• Integrals Class 12 Ex 7.3 in Hindi Medium
• Integrals Class 12 Ex 7.4
• Integrals Class 12 Ex 7.4 in Hindi Medium
• Integrals Class 12 Ex 7.5
• Integrals Class 12 Ex 7.5 in Hindi Medium
• Integrals Class 12 Ex 7.6
• Integrals Class 12 Ex 7.6 in Hindi Medium
• Integrals Class 12 Ex 7.7
• Integrals Class 12 Ex 7.7 in Hindi Medium
• Integrals Class 12 Ex 7.8
• Integrals Class 12 Ex 7.8 in Hindi Medium
• Integrals Class 12 Ex 7.9
• Integrals Class 12 Ex 7.9 in Hindi Medium
• Integrals Class 12 Ex 7.10
• Integrals Class 12 Ex 7.10 in Hindi Medium
• Integrals Class 12 Ex 7.11
• Integrals Class 12 Ex 7.11 in Hindi Medium
• Integrals Class 12 Miscellaneous Exercise
• RD Sharma Class 12 Integrals
• NCERT Exemplar Class 12 Maths Integrals
• Integrals Class 12 Notes Maths Chapter 7
• Important Questions Class 12 Maths Integrals
• JEE Main Mathematics Definite and Indefinite 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:

Question 2.
\(\frac { { \left( logx \right) }^{ 2 } }{ x } \)
Solution:

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

Question 4.
sinx sin(cosx)
Solution:

Question 5.
sin(ax+b) cos(ax+b)
Solution:

Question 6.
\(\sqrt { ax+b } \)
Solution:

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

Question 8.
\(x\sqrt { 1+{ 2x }^{ 2 } } \)
Solution:

Question 9.
\((4x+2)\sqrt { { x }^{ 2 }+x+1 } \)
Solution:

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:

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:

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:

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:

Question 23.
\(\frac { { sin }^{ -1 }x }{ \sqrt { 1-{ x }^{ 2 } } } \)
Solution:

Question 24.
\(\frac { 2cosx-3sinx }{ 6cosx+4sinx }\)
Solution:

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:

Question 29.
cotx log sinx
Solution:

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

Question 31.
\(\frac { sinx }{ { (1+cosx) }^{ 2 } } \)
Solution:

Question 32.
\(\frac { 1 }{ 1+cotx }\)
Solution:

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

Question 34.
\(\frac { \sqrt { tanx } }{ sinxcosx } \)
Solution:

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:

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:

गणित कक्षा 12 समाकलन प्रश्नावली 7.2

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

प्रश्न 1.
\(\frac{2 x}{1+x^{2}}\)
हल-

प्रश्न 2.
\(\frac{(\log x)^{2}}{x}\)
हल-

प्रश्न 3.
\(\frac{1}{x+x \log x}\)
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

प्रश्न 6.
\(\sqrt{a x+b}\)
हल-

प्रश्न 7.
\(x \sqrt{x+2}\)
हल-

प्रश्न 8.
\(x \sqrt{1+2 x^{2}}\)
हल-

प्रश्न 9.
(4x + 2) \(\sqrt{x^{2}+x+1}\)
हल-

प्रश्न 10.
\(\frac{1}{x-\sqrt{x}}\)
हल-

प्रश्न 11.
\(\frac{x}{\sqrt{x+4}}\), x > 0
हल-

प्रश्न 12.
(x³ – 1)^1/3 x⁵
हल-

प्रश्न 13.
\(\frac{x^{2}}{\left(2+3 x^{3}\right)^{3}}\)
हल-

प्रश्न 14
\(\frac{1}{x(\log x)^{m}}\), x > 0, m ≠ 1
हल-

प्रश्न 15
\(\frac{x}{9-4 x^{2}}\)
हल-

प्रश्न 16.
e^2x+3
हल-

प्रश्न 17.
\(\frac{x}{e^{x^{2}}}\)
हल-

प्रश्न 18.
\(\frac{e^{\tan ^{-1} x}}{1+x^{2}}\)
हल-

प्रश्न 19.
\(\frac{e^{2 x}-1}{e^{2 x}+1}\)
हल-

प्रश्न 20.
\(\frac{e^{2 x}-e^{-2 x}}{e^{2 x}+e^{-2 x}}\)
हल-

प्रश्न 21.
tan²(2x – 3)
हल-

प्रश्न 22.
sec²(7 – 4x)
हल-

प्रश्न 23.
\(\frac{\sin ^{-1} x}{\sqrt{1-x^{2}}}\)
हल-

प्रश्न 24.

हल-

प्रश्न 25.

हल-

प्रश्न 26.
\(\frac{\cos \sqrt{x}}{\sqrt{x}}\)
हल-

प्रश्न 27.
\(\sqrt{\sin 2 x} \cdot \cos 2 x\)
हल-

प्रश्न 28.
\(\frac{\cos x}{\sqrt{1+\sin x}}\)
हल-

प्रश्न 29.
cot x log sin x
हल-

प्रश्न 30.
\(\frac{\sin x}{1+\cos x}\)
हल-

प्रश्न 31.
\(\frac{\sin x}{(1+\cos x)^{2}}\)
हल-

प्रश्न 32.
\(\frac{1}{1+\cot x}\)
हल-

प्रश्न 33.
\(\frac{1}{1-\tan x}\)
हल-

प्रश्न 34.
\(\frac{\sqrt{\tan x}}{\sin x \cos x}\)
हल-

प्रश्न 35.
\(\frac{(1+\log x)^{2}}{x}\)
हल-

प्रश्न 36.

हल-

प्रश्न 37.

हल-

प्रश्न 38.

हल-

प्रश्न 39.
\(\int \frac{d x}{\sin ^{2} x \cos ^{2} x}\) बराबर है-
(A) tan x + cot x + C
(B) tan x – cotx + C
(C) tan x cot x + C
(D) tan x – cot 2x + C
हल-