Class 12 Mathematics

Integrals

NCERT Exercise 7.1

Find an anti derivative (or integral) of the following by the method of inspection:

Question: (1) Sin2x

Solution:

Given, sin2x

To find out the antiderivation we have to find out a function whose derivation is sin2x.

Integrals NCERT Exercise 7.1 class twelve math1

Therefore, antiderivaion of

Integrals NCERT Exercise 7.1 class twelve math2

Alternate method:

Integrals NCERT Exercise 7.1 class twelve math3

Therefore, antiderivaion of

Integrals NCERT Exercise 7.1 class twelve math4

Question: (2) Cos 3x

Solution:

Given, cos3x

Since,

Integrals NCERT Exercise 7.1 class twelve math6

Thus, antiderivative of Integrals NCERT Exercise 7.1 class twelve math8

Alternate method:

Integrals NCERT Exercise 7.1 class twelve math7

Thus, antiderivative of Integrals NCERT Exercise 7.1 class twelve math8_1

Integrals NCERT Exercise 7.1 class twelve math9
Integrals NCERT Exercise 7.1 class twelve math10

Therefore, antiderivative of Integrals NCERT Exercise 7.1 class twelve math11

Alternate method:

Integrals NCERT Exercise 7.1 class twelve math12

Therefore, antiderivative of Integrals NCERT Exercise 7.1 class twelve math11_1



Integrals NCERT Exercise 7.1 class twelve math13
Integrals NCERT Exercise 7.1 class twelve math14

Therefore, antiderivative of Integrals NCERT Exercise 7.1 class twelve math15

Alternate method:

Integrals NCERT Exercise 7.1 class twelve math16

Therefore, antiderivative of Integrals NCERT Exercise 7.1 class twelve math15_1


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