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

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

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
B
`intsqrt(1+sin((x)/(4)))dx=intsqrt(1+2sin.(x)/(8)+cos.(x)/(8))dx`
`=intsqrt(sin^(2).(x)/(8)+cos^(2).(x)/(8)+2sin.(x)/(8)cos.(x)/(8))dx`
`=intsqrt((sin.(x)/(8)+cos.(x)/(8))^(2))dx`
`=int(sin.(x)/(8)+cos.(x)/(8))dx`
`=(-cos.(x)/(8))/(1//8)+(sin.(x)/(8))/(1//8)+C`
`=8(sin.(x)/(8)-cos.(x)/(8))+C`
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