2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.1

Students can Download Maths Chapter 7 Integrals Ex 7.1 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 7.1

2nd PUC Maths Integrals NCERT Text Book Questions and Answers Ex 7.1

Find an anti derivative (of integral) of the following functions by the method of inspection.

Question 1.
sin 2x
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.1.1

Question 2.
cos 3x
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.1.2

Question 3.
e2x
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.1.3

Question 4.
(ax + b)2
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.1.4

Question 5.
sin 2x – 4 e3x
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.1.5

KSEEB Solutions

Find the following integrals in Exercises 6 to 20:

Question 6.
(4e3x + 1)dx
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.1.6

Question 7.
\(\int x^{2}\left(1-\frac{1}{x^{2}}\right) d x\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.1.7

Question 8.
∫(ax2 + bx+c)dx
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.1.8

Question 9.
∫(2x2+ex)dx
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.1.9

KSEEB Solutions

Question 10.
\(\int\left(\sqrt{x}-\frac{1}{\sqrt{x}}\right)^{2} d x\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.1.10

Question 11.
\(\int \frac{x^{3}+5 x^{2}-4}{x^{2}} d x\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.1.11

Question 12.
\(\int \frac{x^{3}+3 x+4}{\sqrt{x}} d x\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.1.12

Question 13.
\(\int \frac{x^{3}-x^{2}+x-1}{x-1} d x\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.1.13

Question 14.
\(\int(1 – x) \sqrt{x} d x\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.1.14

Question 15.
\(\int \sqrt{x}\left(3 x^{2}+2 x+3\right) d x\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.1.15

Question 16.
∫(2x – 3cosx + ex)dx
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.1.16

Question 17.
\(\int\left(2 x^{2}-3 \sin x+5 \sqrt{x}\right) d x\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.1.17

Question 18.
∫sec x(sec x + tan x)dx
Answer:
∫sec x (sec x + tan x) dx
= ∫(sec2x+sec x tan x) dx
= tan x + sec x + C

KSEEB Solutions

Question 19.
\(\int \frac { \sec ^{ 2 } x }{ { cosec }^{ 2 }x } dx\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.1.18

Question 20.
\(\int \frac{2-3 \sin x}{\cos ^{2} x} d x\)
Answer:
∫(2sec2 x – 3sec x tan x)dx
= 2 tan x – 3 sec x + C

Choose the correct answer in Exercises 21 and 22.

Question 21.
The anti derivative of \(\left(\sqrt{x}+\frac{1}{\sqrt{x}}\right)\) equals
(A) \(\frac{1}{3} x^{\frac{1}{3}}+2 x^{\frac{1}{2}}+C\)
(B) \(\frac{2}{3} x^{\frac{2}{3}}+\frac{1}{2} x^{2}+C\)
(C) \(\frac{2}{3} x^{\frac{3}{2}}+2 x^{\frac{1}{2}}+C\)
(D) \(\frac{3}{2} x^{\frac{3}{2}}+\frac{1}{2} x^{\frac{1}{2}}+C\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.1.19

Question 22.
\(\frac{d}{d x} f(x)=4 x^{3} \cdot \frac{3}{x^{4}}\) such that f(2) Then f(x) is ………
(A)\(x^{4}+\frac{1}{x^{3}}-\frac{129}{8}\)
(B)\(x^{3}+\frac{1}{x^{4}}+\frac{129}{8}\)
(C)\(x^{4}+\frac{1}{x^{3}}+\frac{129}{8}\)
(D)\(x^{3}+\frac{1}{x^{4}}-\frac{129}{8}\)
Answer:
2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.1.20

Leave a Comment

error: Content is protected !!