First slide

Methods of integration

Question

If $\int \frac{s i n^{2} x}{1 + s i n^{2} x} d x = x - K t a n^{- 1} (M t a n x) + C$ then

Easy

A

$M = \frac{1}{\sqrt{2}}$
B

$K = \frac{1}{\sqrt{2}}$
C

$M = - \frac{1}{\sqrt{2}}$
D

$K = - \frac{1}{\sqrt{2}}$

Solution

$\frac{\sin^{2} x}{1 + \sin^{2} x} = 1 - \frac{1}{1 + \sin^{2} x} = 1 - \frac{\sec^{2} x}{1 + 2 \tan^{2} x}$
So $\int \frac{\sin^{2} x}{1 + \sin^{2} x} = x - \frac{1}{\sqrt{2}} \tan^{- 1} (\sqrt{2} \tan x) + C .$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App