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If int f(x) sinx cosx dx=(1)/(2(b^(2)-a...

If `int f(x) sinx cosx dx=(1)/(2(b^(2)-a^(2))) "In " f(x)+c," then " f(x)` is equal to

A

`(1)/(a^(2)sin^(2)x+b^(2)cos^(2)x)`

B

`(1)/(a^(2)sin^(2)x-b^(2)cos^(2)x)`

C

`(1)/(a^(2)cos^(2)x+b^(2)sin^(2)x)`

D

`(1)/(a^(2)cos^(2)x-b^(2)sin^(2)x)`

Text Solution

Verified by Experts

The correct Answer is:
A
Differentiating, we get
`(f'(x))/(f(x)^(2))=2(b^(2)-a^(2)) sin x cosx`
Intergrating both sides w.r.t. x we get
` -(1)/(f(x))= -b^(2) cos^(2)x-a^(2)sin^(2)x`
or `f(x)=(1)/(a^(2)sin^(2)x+b^(2)cos^(2)x)`
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