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int((sin theta+cos theta))/(sqrt(sin 2th...

`int((sin theta+cos theta))/(sqrt(sin 2theta))d theta` is equal to

A

`log |cos theta-sin theta+sqrt(sin 2 theta)|+C`

B

`log|sin theta - cos theta+sqrt(sin 2 theta)|+C`

C

`sin^(-1)(sin theta+cos theta)+C`

D

`sin^(-1)(sin theta +cos theta)+C`

Text Solution

Verified by Experts

The correct Answer is:
C
Let `l=int(sin theta+cos theta)/(sqrt(1+sin 2 theta-1))d theta`
`=int (sin theta+cos theta)/(sqrt(1-(sin theta-cos theta)^(2)))d theta`
`"Put "sin theta - cos theta=t`
`rArr" "l=int(1)/(sqrt(1-t^(2)))dt = sin^(-1)t+C`
`=sin^(-1)(sin theta - cos theta)+C`
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