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intsqrt(1+sin((x)/(4)))dx is equal to...

`intsqrt(1+sin((x)/(4)))dx` is equal to

A

`B(sin.(x)/(8)-cos.(x)/(8))+c`

B

`(sin.(x)/(8)+cos.(x)/(8))+c`

C

`(1)/(8)(sin.(x)/(8)-cos.(x)/(8))+c`

D

`8(cos.(x)/(8)-sin.(x)/(8))+c`

Text Solution

Verified by Experts

The correct Answer is:
A
We know that ,
`sqrt(1+sin2theta)=sintheta+costheta`
`intsqrt(1+sin.(x)/(4))dx`
`=int(sin.(x)/(8) +cos.(x)/(8))dx`
`=-8cos.(x)/(8)+8sin.(x)/(8)+c`
`=8(sin.(x)/(8)-cos.(x)/(8))+c`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-PRACTICE SET 02-Paper 2 (Mathematics )
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