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If intf(x)dx=g(x), then intf(x)g(x)dx is...

If `intf(x)dx=g(x),` then `intf(x)g(x)dx` is equal to

A

`(1)/(2)f^(2)f(x)`

B

`(1)/(2)g^(2)(x)`

C

`(1)/(2)[g'(x)]^(2)`

D

`f'(x)g(x)`

Text Solution

Verified by Experts

The correct Answer is:
B
Given, `intf(x)dx=g(x)`
`therefore" "g'(x)=f(x)`
On using integration by parts, we get
`intf(x)g(x)dx=g(x)int f(x)dx-int[g'(x)int f(x)dx]dx`
`=g(x)g(x)-intg'(x)g(x)dx`
`=[g(x)]^(2)-[f(x)g(x)dx`
`rArr" "[f(x)g(x)dx=(1)/(2)][g(x)]^(2)`
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