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If intf(x)sinxcosxdx=1/(2(b^2-a^2))lnf(x...

If `intf(x)sinxcosxdx=1/(2(b^2-a^2))lnf(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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CENGAGE ENGLISH-INDEFINITE INTEGRATION-EXERCISES (Single Correct Answer Type)
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  18. If I=inte^(-x)log(e^x+1)dx ,t h e nIe q u a l a+(e^(-x)+1)log(e^x+1)...

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  19. "If " int x e^(x) cosx dx=ae^(x)(b(1-x)sinx+cx cosx)+d, then

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