First slide

Introduction to integration

Question

$\int \frac{S i n^{- 1} x - C o s^{- 1} x}{S i n^{- 1} x + C o s^{- 1} x} d x =$

Easy

A

$\frac{4}{π} [x S i n^{- 1} x + \sqrt{1 - x^{2}}] - x + c$
B

$\frac{1}{π} [x S i n^{- 1} x + \sqrt{1 - x^{2}}] - x + c$
C

$\frac{2}{π} [x S i n^{- 1} x + \sqrt{1 - x^{2}}] - x + c$
D

$\frac{2}{π} [x S i n^{- 1} x - \sqrt{1 - x^{2}}] - x + c$

Solution

$\int \frac{2 \sin^{- 1} x - \frac{π}{2}}{\frac{π}{2}} d x$ $= \frac{2}{π} 2 \int \sin^{- 1} x d x - \int 1 d x$
$= \frac{4}{π} [\sin^{- 1} x . x - \int \frac{x}{\sqrt{1 - x^{2}}} d x] - x$
$= \frac{4}{π} [x \sin^{- 1} x + \frac{1}{2} \int \frac{- 2 x}{\sqrt{1 - x^{2}}} d x] - x$
= $\frac{4}{π} [x \sin^{- 1} x + \frac{1}{2} 2 \sqrt{1 - x^{2}}] - x + c u \sin g \int \frac{d t}{\sqrt{t}} = 2 \sqrt{t}$
$= \frac{4}{π} [x \sin^{- 1} x + \sqrt{1 - x^{2}}] - x + c$

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