2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.6

Students can Download Maths Chapter 7 Integrals Ex 7.6 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 7.6

2nd PUC Maths Integrals NCERT Text Book Questions and Answers Ex 7.6

Integrate the functions in Exercises 1 to 22.

Question 1.
x sin x
Answer:
∫ x sin x . dx
= x(-cosx) +∫ 1 x cos x dx
= – x cos x + sin x + C

Question 2.
x sin 3x
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.6.1

Question 3.
x2ex
Answer:
∫ x2ex.dx
= x2ex -∫2x x ex dx = x2ex -2(xex -1 x ex)
= x2ex – 2x ex + 2ex +C
= ex (x2 – 2x + 2) + C

KSEEB Solutions

Question 4.
x log x
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.6.2
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.6.3

Question 5.
x log 2x
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.6.4

Question 6.
x2 log x
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.6.5

Question 7.
x sin-1 x
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.6.6

KSEEB Solutions

Question 8.
x tan-1 x
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.6.7
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.6.8

Question 9.
x cos-1 x
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.6.9

Question 10.
(sin-1 x)2
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.6.10

Question 11.
\(\frac{x \cos ^{-1} x}{\sqrt{1-x^{2}}}\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.6.11
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.6.12

KSEEB Solutions

Question 12.
x sec-2 x
Answer:
sec2x
= x tan x -∫tan x + dx
= x tan x + log |cos x| +C

Question 13.
tan-1 x
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.6.13

Question 14.
x(log x)2
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.6.14

Question 15.
(x2 + 1) log x
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.6.15
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.6.16

Question 16.
ex (sin x + cos x)
Answer:
∫ex (sin x + cos x) dx
put f(x) = sin x
f’(x) = cos x
= ∫ex (f(x) + f’(x)) dx = e’f(x) + C
=∫ex (sinx + cosx) dx = ex sin x + C

KSEEB Solutions

Question 17.
\(\frac{\mathbf{x} \mathbf{e}^{\mathbf{x}}}{(\mathbf{1}+\mathbf{x})^{2}}\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.6.17

Question 18.
\(\mathbf{e}^{x}\left(\frac{1+\sin x}{1+\cos x}\right)\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.6.18
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.6.19

Question 19.
\(e^{x}\left(\frac{1}{x}-\frac{1}{x^{2}}\right)\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.6.20

Question 20.
\(\frac{(x-3) e^{x}}{(x-1)^{3}}\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.6.21

KSEEB Solutions

Question 21.
e2x sin x
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.6.22
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.6.23

Question 22.
\(\sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right)\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.6.24

Question 23.
\(\int x^{2} e^{x^{2}} d x \text { equals }\)
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.6.25
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.6.26

Question 24.
∫ex sec x (1+ tan x) dx equals
(A) ex cos x+ C
(B) ex sec x+ C
(C) ex sin x+ C
(D) ex tan x+ C
Answer:
∫ex sec x (1 + tan x) dx
= ∫ex (sec x + sec x tan x) dx
put f (x 0 = sec x, f’ (x) = sec x tan x
= ∫ ex (sec x + sec x tan x) dx = ex sec x + C
Answer (B)

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