First slide

Evaluation of definite integrals

Question

$\int_{0}^{\sin^{2} x} \sin^{- 1} \sqrt{t} d t + \int_{0}^{\cos^{2} x} \cos^{- 1} \sqrt{t} d t =$

Moderate

A

$\frac{π}{4}$
B

$\frac{π}{3}$
C

$\frac{π}{2}$
D

$π$

Solution

$Let t = \sin^{2} u in the first integral and t = \cos^{2} u in the second integral. Then$
$I_{1} + I_{2} = \int_{0}^{x} u \sin 2 u d u - \int_{π / 2}^{x} u \sin 2 u d u$
$\Rightarrow I_{1} + I_{2} = \int_{0}^{x} u \sin 2 u d u + \int_{x}^{π / 2} u \sin 2 u d u = \int_{0}^{π / 2} u \sin 2 u d u$
$= {(- \frac{u}{2} \cos 2 u + \frac{1}{4} \sin 2 u)}_{0}^{\frac{π}{2}}$
= $\frac{π}{4}$

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