2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.11

Students can Download Maths Chapter 7 Integrals Ex 7.11 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 7.11

2nd PUC Maths Integrals NCERT Text Book Questions and Answers Ex 7.11

By using the properties of definite integrals, evaluate the integrals in Exercises 1 to 19.

Question 1.
\(\int_{0}^{\frac{\pi}{2}} \cos ^{2} x d x\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.11.1

Question 2.
\(\int_{0}^{\frac{\pi}{2}} \frac{\sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}} d x\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.11.2

KSEEB Solutions

Question 3.
\(\int_{0}^{\frac{\pi}{2}} \frac{\sin ^{\frac{3}{2}} x d x}{\sin ^{\frac{3}{2}} x+\cos ^{\frac{3}{2}} x} d x\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.11.3

Question 4.
\(\int_{0}^{\frac{\pi}{2}} \frac{\cos ^{5} x d x}{\sin ^{5} x+\cos ^{5} x}\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.11.4

Question 5.
\(\int_{-5}^{5}|x+2| d x\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.11.5

Question 6.
\(\int_{2}^{8}|x-5| d x\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.11.6
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.11.7

KSEEB Solutions

Question 7.
\(\int_{0}^{1} x(1-x)^{n} d x\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.11.8

Question 8.
\(\int_{0}^{\frac{\pi}{4}} \log (1+\tan x) d x\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.11.9

Question 9.
\(\int_{0}^{2} x \sqrt{2-x} d x\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.11.10

Question 10.
\(\int_{0}^{\frac{\pi}{2}}(2 \log \sin x-\log \sin 2 x) d x\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.11.11

KSEEB Solutions

Question 11.
\(\int_{\frac{-\pi}{2}}^{\frac{\pi}{2}} \sin ^{2} x d x\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.11.12

Question 12.
\(\int_{0}^{\pi} \frac{\mathbf{x} \mathbf{d} \mathbf{x}}{1+\sin \mathbf{x}}\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.11.13

Question 13.
\(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \sin ^{7} x d x\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.11.14

Question 14.
\(\int_{0}^{2 \pi} \cos ^{5} x d x=I\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.11.15

KSEEB Solutions

Question 15.
\(\int_{0}^{\frac{\pi}{2}} \frac{\sin x-\cos x}{1+\sin x \cos x} d x\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.11.16

Question 16.
\(\int_{0}^{\pi} \log (1+\cos x) d x\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.11.17
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.11.18

Question 17.
\(\int_{0}^{\mathrm{a}} \frac{\sqrt{\mathbf{x}}}{\sqrt{\mathbf{x}}+\sqrt{\mathbf{a}-\mathbf{x}}} \mathbf{d} \mathbf{x}\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.11.19

Question 18.
\(\int_{0}^{4}|x-1| d x\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.11.20
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.11.21

KSEEB Solutions

Question 19.
Show that \(\int_{0}^{a} f(x) g(x) d x=2 \int_{0}^{a} f(x) d x\) if f and g are defined as f(x) = f(a – x) and g(x) + g(a – x) = 4 . Choose the correct answer in Exercises 20 and 21
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.11.22

Question 20.
The value \(\int_{\frac{-\pi}{2}}^{\frac{\pi}{2}}\left(x^{3}+x \cos x+\tan ^{3} x+1\right) d x\) dx is……..
(A) 0
(B) 2
(C) π
(D) 1
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.11.23

Question 21.
The Value of \(\int_{0}^{\frac{\pi}{2}} \log \left(\frac{4+3 \sin x}{4+3 \cos x}\right) d x\)
(A) 2
(B) \(\frac{3}{4}\)
(C) 0
(D) -2
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.11.24
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.11.25

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