First slide

Evaluation of definite integrals

Question

$\int_{- π}^{π} (\cos p x - \sin q x)^{2} d x$ where $p$ and $q$ are in tegers is equal to

Moderate

A

$- π$
B

0
C

$π$
D

2 $π$

Solution

$I = \int_{- π}^{π} [\cos^{2} p x + \sin^{2} q x - 2 \cos p x \sin q x] d x$
$= \int_{0}^{π} [2 + \cos 2 p x - \cos 2 q x] d x = 2 π$
$[∵$ third term in the integrand is odd]

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