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If a function f(x) satisfies f'(x)=g(x)....

If a function f(x) satisfies `f'(x)=g(x)`. Then, the value of `int_(a)^(b)f(x)g(x)dx` is

A

`(1)/(2)[{(f(b)}^(2)-{f(a)}^(2)]`

B

`(1)/(2)[{f(b)}^(2)+{f(a)}^(2)]`

C

`(1)/(2)[f(b)-f(a)]^(2)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
`because f'(x)=g(x)`
`impliesint_(a)^(b)f(x)g(x)dx=int_(a)^(b)f(x)f'(x)dx`
`=[({f(x)}^(2))/(2)]_(a)^(b)`
`=(1)/(2)[f(b)}^(2)-{f(a)]^(2)]`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-PRACTICE SET 06-PAPER 2 (MATHEMATICS)
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