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Let `f(x)` be a function satisfying `f\'(x)=f(x)` with `f(0)=1` and `g(x)` be the function satisfying `f(x)+g(x)=x^2`. Then the value of integral `int_0^1 f(x)g(x)dx` is equal to (A) `(e-2)/4` (B) `(e-3)/2` (C) `(e-4)/2` (D) none of these

A

`e-(1)/(2)e^(2) -(5)/(2)`

B

`e-e^(2)-3`

C

`(1)/(2)(e-3)`

D

`e-(1)/(2) e^(2) - (3)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
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