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If f(x)dx=g(x) and f^(-1)(x) is differen...

If `f(x)dx=g(x) and f^(-1)(x)` is differentiable, then `intf^(-1)(x)dx` equal to

A

`g^(-1)(x)+C`

B

`xf^(-1)+C`

C

`xf^(-1)(x)-g(f^(-1)(x))+C`

D

`f^(-1)(x)+C`

Text Solution

Verified by Experts

The correct Answer is:
C
`I=intf^(-1)(x)dx=f^(-1)(x).x-intx.((f^(-1))(x))'dx`
Put `f^(-1)(x)=t`
`therefore" "I=f^(-1)(x).x-intf(t).dt`
`therefore" "I=f^(-1).x-g(t)+C`
`=x.f^(-1)(x)-g(f^(-1)(x))+C`
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