# 2nd PUC Maths Question Bank Chapter 7 Integrals Ex 7.1

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## 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

Question 2.
cos 3x

a

Question 3.
e2x

Question 4.
(ax + b)2

Question 5.
sin 2x – 4 e3x

Find the following integrals in Exercises 6 to 20:

Question 6.
(4e3x + 1)dx

Question 7.
$$\int x^{2}\left(1-\frac{1}{x^{2}}\right) d x$$

Question 8.
∫(ax2 + bx+c)dx

Question 9.
∫(2x2+ex)dx

Question 10.
$$\int\left(\sqrt{x}-\frac{1}{\sqrt{x}}\right)^{2} d x$$

Question 11.
$$\int \frac{x^{3}+5 x^{2}-4}{x^{2}} d x$$

Question 12.
$$\int \frac{x^{3}+3 x+4}{\sqrt{x}} d x$$

Question 13.
$$\int \frac{x^{3}-x^{2}+x-1}{x-1} d x$$

Question 14.
$$\int(1 – x) \sqrt{x} d x$$

Question 15.
$$\int \sqrt{x}\left(3 x^{2}+2 x+3\right) d x$$

Question 16.
∫(2x – 3cosx + ex)dx

Question 17.
$$\int\left(2 x^{2}-3 \sin x+5 \sqrt{x}\right) d x$$

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

Question 19.
$$\int \frac { \sec ^{ 2 } x }{ { cosec }^{ 2 }x } dx$$

Question 20.
$$\int \frac{2-3 \sin x}{\cos ^{2} x} d x$$
∫(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) $$\frac{3}{2} x^{\frac{3}{2}}+\frac{1}{2} x^{\frac{1}{2}}+C$$
$$\frac{d}{d x} f(x)=4 x^{3} \cdot \frac{3}{x^{4}}$$ 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)$$x^{3}+\frac{1}{x^{4}}-\frac{129}{8}$$