First slide

Methods of integration

Question

$Evaluate \int e^{x} (\frac{1 - \sin x}{1 - \cos x}) d x$

Easy

A

$e^{x} \cot \frac{x}{2} + c$
B

$- e^{x} \cot \frac{x}{2} + c$
C

$- e^{x} \cot x + c$
D

None of these

Solution

$\begin{array}{l} = \int e^{x} (\frac{1 - \sin x}{1 - \cos x}) d x \\ = \int e^{x} (\frac{1 - 2 \sin \frac{x}{2} \cos \frac{x}{2}}{2 \sin^{2} \frac{x}{2}}) d x \\ \begin{array}{l} = \int e^{x} (\frac{1}{2} {cosec}^{2} \frac{x}{2} - \cot \frac{x}{2}) d x \\ = - \int e^{x} (\cot \frac{x}{2} + {(\cot \frac{x}{2})}^{'}) d x u \sin g t h e f o r m u l a \int e^{x} (f (x) + f^{'} (x)) d x = e^{x} f (x) + C \\ = - e^{x} \cot \frac{x}{2} + c \end{array} \end{array}$

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