2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2

Students can Download Maths Chapter 7 Integrals Ex 7.2 Questions and Answers, Notes Pdf, 2nd PUC Maths Question Bank with Answers helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.

Karnataka 2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2

2nd PUC Maths Integrals NCERT Text Book Questions and Answers Ex 7.2

Integrate the function in Exercises 1 to 37:

Question 1.
\(\cfrac{2 x}{1+x^{2}}\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.1

Question 2.
\(\cfrac{(\log x)^{2}}{x}\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.2

Question 3.
\(\cfrac{1}{x+x \log x}\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.3

Question 4.
sin x sin (cos x)
Answer:
∫ sinx sin (cosx) dx
cosx = t ⇒ – sinx . dx = dt
∫- sin t. dt = cos t + C = cos (cos x) + C

KSEEB Solutions

Question 5.
sin (ax + b) cos (ax + b)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.4

Question 6.
\(\sqrt{a x+b}\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.5
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.6

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

2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.7

Question 8.
\(x \sqrt{1+2 x^{2}}\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.8

KSEEB Solutions

Question 9.
\((4 x+2) \sqrt{x^{2}+x+1}\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.9

Question 10.
\(\frac{1}{x-\sqrt{x}}\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.10
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.11

Question 11.
\(\frac{\mathbf{x}}{\sqrt{\mathbf{x}+4}}, \mathbf{x}>0\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.12

Question 12.
\(\frac{\mathbf{x}}{\sqrt{\mathbf{x}+4}}, \mathbf{x}>0\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.13
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.14

Question 13.
\(\frac{x^{2}}{\left(2+3 x^{3}\right)^{3}}\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.15

Question 14.
\(\frac{1}{\mathbf{x}(\log \mathbf{x})^{\mathrm{m}}} \mathbf{x}>0\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.16

Question 15.
\(\frac{x}{9-4 x^{2}}\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.17

KSEEB Solutions

Question 16.
e2x + 3
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.18
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.19

Question 17.
\(\frac{\mathbf{x}}{\mathbf{c}^{x^{2}}}\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.20

Question 18.
\(\frac{e^{\tan ^{-1} x}}{1+x^{2}}\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.21

Question 19.
\(\frac{e^{2 x}-1}{e^{2 x}+1}\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.22

Question 20.
\(\frac{e^{2 x}-e^{-2 x}}{e^{2 x}+e^{-2 x}}\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.23

KSEEB Solutions

Question 21.
tan2 (2x – 3)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.24

Question 22.
sec2 (7 – 4x)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.25

Question 23.
\(\frac{\sin ^{-1} x}{\sqrt{1-x^{2}}}\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.26

Question 24.
\(\frac{2 \cos x-3 \sin x}{6 \cos x+4 \sin x}\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.27
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.28

Question 25.
\(\frac{1}{\cos ^{2} x(1-\tan x)^{2}}\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.29

 

KSEEB Solutions

Question 26.
\(\frac{\cos \sqrt{x}}{\sqrt{x}}\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2 29

Question 27.
\(\sqrt{\sin 2 x} \cos 2 x\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.30
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.31

Question 28.
\(\frac{\cos x}{\sqrt{1+\sin x}}\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.32

Question 29.
cot x log sin x
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.33

Question 30.
\(\frac{\sin x}{(1+\cos x)^{2}}\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.34

Question 31.
\(\frac{\sin x}{(1+\cos x)^{2}}\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.35

KSEEB Solutions

Question 32.
\(\frac{1}{1+\cot x}\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.36
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.37

Question 33.
\(\frac{1}{1-\tan x}\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.38

Question 34.
\(\frac{\sqrt{\tan x}}{\sin x \cos x}\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.39

Question 35.
\(\frac{(1+\log x)^{2}}{x}\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.40

Question 36.
\(\frac{(x+1)(x+\log x)^{2}}{x}\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.41

Question 37.
\(\frac{x^{3} \sin \left(\tan ^{-1} x^{4}\right)}{1+x^{8}}\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.42

Question 38.
\(\int \frac { 10x^{ 9 }+10^{ x }\log _{ x^{ 10 } } dx }{ x^{ 10 }+10^{ x } } { equals }\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.43
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.44
KSEEB Solutions

Question 39.
\(\int \frac{d x}{\sin ^{2} x \cos ^{2} x} \text { equals }\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.2.45

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