First slide

Introduction to integration

Question

$\int \frac{x \sin^{- 1} x}{\sqrt{1 - x^{2}}} d x =$

Moderate

A

$- x - \sqrt{1 - x^{2}} \sin^{- 1} x + c$
B

$\frac{x}{2} - \sqrt{1 - x^{2}} \sin^{- 1} x + c$
C

$x + \sqrt{1 - x^{2}} \sin^{- 1} x + c$
D

$x - \sqrt{1 - x^{2}} \sin^{- 1} x + c$

Solution

$f (x) = \sin^{- 1} x \cdot g (x) = \frac{x}{\sqrt{1 - x^{2}}} By using integration by parts$
$\int \frac{x \sin^{- 1} x}{\sqrt{1 - x^{2}}} d x = \sin^{- 1} x (- \sqrt{1 - x^{2}}) - \int \frac{1}{\sqrt{1 - x^{2}}} (- 1) \sqrt{1 - x^{2}} d x = x - \sqrt{1 - x^{2}} \sin^{- 1} x + c$

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