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Let f(x) be a function satisfying f'(x) ...

Let `f(x)` be a function satisfying `f'(x) = f(x)` with `f(0) = 1 and g(x)` be a function that satisfies `f(x) + g(x) = x^2`. Then the value of the integral `int_0^1 f(x) g (x) dx` is :

A

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

B

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

C

`e + (e^2)/2 + 5/2`

D

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

Text Solution

Verified by Experts

The correct Answer is:
B
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