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Let f : [0, 2]to R be a function which i...

Let `f : [0, 2]to R` be a function which is continuous on `[0, 2]` and is differentiable on `(0, 2)` with `f(0)=1`. Let `F(x)=int_(0)^(x^(2))f(sqrt(t))dt`, for `x in [0, 2]`. If `F'(x)=f'(x), AA x in (0, 2)`, then F (2) equals :

A

`e^(2)-1`

B

`e^(4)-1`

C

`e-1`

D

`e^(4)`

Text Solution

Verified by Experts

The correct Answer is:
B
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