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"If " int sqrt(1+sinx) f(x)dx=(2)/(3)(1+...

`"If " int sqrt(1+sinx) f(x)dx=(2)/(3)(1+sinx)^(3//2)+c, " then " f(x) " equals "`

A

`cos x`

B

`sin x`

C

`tan x`

D

`1`

Text Solution

Verified by Experts

The correct Answer is:
A
`" Differentiating both sides, we get "`
` sqrt(1+sinx)f(x)=(2)/(3)(3)/(2)(1+sinx)^(1//2)cosx`
`"or "f(x)=cosx`
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