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Evaluate: int(sqrt((cosx)/(x))-sqrt((x)/...

Evaluate: `int(sqrt((cosx)/(x))-sqrt((x)/(cosx))sinx)dx` equals

A

`-sqrt(xcosx)+C`

B

`sqrt(xsinx)+C`

C

`2sqrt(xcos x)+C`

D

`C-2sqrt(xcosx)`

Text Solution

Verified by Experts

The correct Answer is:
C
`I=int(cosx-x sin x)/(sqrt(xcosx))dx`
Put `xcosx=t^(2)`
`rArr" "(cosx-x sin x)dx=2t dt`
`rArr" "I=int(2tdt)/(t)=2t+C=2sqrt(x cos x)+C`
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