NCERT Class 12 Part 2 - Math

Pawan K. Jain

Chapter 7

Integrals - all with Video Answers

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Section 1

Introduction

Problem 1

Find an anti derivative (or integral) of the following functions by the method of inspection.
$\sin 2 x$

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Problem 2

Find an anti derivative (or integral) of the following functions by the method of inspection.
$\cos 3 x$

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Problem 3

Find an anti derivative (or integral) of the following functions by the method of inspection.
$e^{2 x}$

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Problem 4

Find an anti derivative (or integral) of the following functions by the method of inspection.
$(a x+b)^{2}$

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Problem 5

Find an anti derivative (or integral) of the following functions by the method of inspection.
$\sin 2 x-4 e^{3 x}$

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Problem 6

Find the following integrals.
$$
\int\left(4 e^{3 x}+1\right) d x
$$

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Problem 7

Find the following integrals.
$$
\int x^{2}\left(1-\frac{1}{x^{2}}\right) d x
$$

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Problem 8

Find the following integrals.
$$
\int\left(a x^{2}+b x+c\right) d x
$$

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Problem 9

Find the following integrals.
$$
\int\left(2 x^{2}+e^{x}\right) d x
$$

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Problem 10

Find the following integrals.
$$
\int\left(\sqrt{x}-\frac{1}{\sqrt{x}}\right)^{2} d x
$$

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Problem 11

Find the following integrals.
$$
\int \frac{x^{3}+5 x^{2}-4}{x^{2}} d x
$$

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Problem 12

Find the following integrals.
$$
\int \frac{x^{3}+3 x+4}{\sqrt{x}} d x
$$

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Problem 13

Find the following integrals.
$$
\int \frac{x^{3}-x^{2}+x-1}{x-1} d x
$$

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Problem 14

Find the following integrals.
$$
\int(1-x) \sqrt{x} d x
$$

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Problem 15

Find the following integrals.
$$
\int \sqrt{x}\left(3 x^{2}+2 x+3\right) d x
$$

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Problem 16

Find the following integrals.
$$
\int\left(2 x-3 \cos x+e^{x}\right) d x
$$

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Problem 17

Find the following integrals.
$$
\int\left(2 x^{2}-3 \sin x+5 \sqrt{x}\right) d x
$$

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Problem 18

Find the following integrals.
$$
\int \sec x(\sec x+\tan x) d x
$$

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Problem 19

Find the following integrals.
$$
\int \frac{\sec ^{2} x}{\operatorname{cosec}^{2} x} d x
$$

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Problem 20

Find the following integrals.
$$
\int \frac{2-3 \sin x}{\cos ^{2} x} d x
$$

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Problem 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) $\frac{2}{3} x^{\frac{2}{3}}+\frac{1}{2} x^{2}+\mathrm{C}$
(C) $\frac{2}{3} x^{\frac{3}{2}}+2 x^{\frac{1}{2}}+C$
(D) $\frac{3}{2} x^{\frac{3}{2}}+\frac{1}{2} x^{\frac{1}{2}}+C$

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Problem 22

If $\frac{d}{d x} f(x)=4 x^{3}-\frac{3}{x^{4}}$ such that $f(2)=0$. 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) $x^{3}+\frac{1}{x^{4}}-\frac{129}{8}$

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