First slide

Methods of integration

Question

$\int \frac{\sqrt{\cos e c x}}{\tan x} d x =$

Moderate

A

$\frac{2}{\sqrt{\cos x}} + C$
B

$\frac{- 2}{\sqrt{\sin x}} + C$
C

$2 \sqrt{\sin x} + C$
D

$2 \sqrt{\cos x} + C$

Solution

$\begin{array}{l} I = \int \frac{\sqrt{\cos e c x}}{\tan x} d x \\ = \int \frac{\cos x}{(\sin x)^{\frac{3}{2}}} d x \\ Let \sin x = t \\ \cos x d x = d t \\ I = \int t^{\frac{- 3}{2}} d t = \frac{t^{1 - \frac{3}{2}}}{1 - \frac{3}{2}} + C \end{array}$
$\begin{array}{l} = \frac{- 2}{\sqrt{t}} + C = \frac{- 2}{\sqrt{\sin x}} + C \\ Level of question: Moderate \end{array}$

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