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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
Given , f ' (x) = g(x)
` int _(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-DEFINITE INTEGRALS-MHT CET Corner
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