First slide

Evaluation of definite integrals

Question

The value of $\int_{- π / 2}^{π / 2} \cos t \sin (2 t - π / 4) d t$ is

Moderate

A

$- 1 / 3$
B

$1 / 3$
C

$\sqrt{2} / 3$
D

$- \sqrt{2} / 3$

Solution

$\begin{array}{l} \int_{- π / 2}^{π / 2} \cos t \sin (2 t - \frac{π}{4}) d t \\ = \frac{1}{\sqrt{2}} \int_{- π / 2}^{π / 2} \cos t (\sin 2 t - \cos 2 t) d t \\ = - \frac{1}{\sqrt{2}} \int_{- π / 2}^{π / 2} \cos t \cos 2 t d t \\ = - \frac{\sqrt{2}}{2} \int_{0}^{π / 2} (\cos 3 t + \cos t) d t \\ = - \frac{1}{\sqrt{2}} (- \frac{1}{3} + 1) = - \frac{1}{\sqrt{2}} \cdot \frac{2}{3} = - \frac{\sqrt{2}}{3} \end{array}$

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