Let f be continuous on...... | JEE Advanced 2014 | Functions

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JEE Advanced 2014

Paper-2 2014

Question

Let $f:[0,2] \rightarrow R$ be a function which is continuous on $[0,2]$ and is differentiable on $(0,2)$ with $f(0)=1$. Let $F(x)=\int_0^{x^2} f(\sqrt{t}) d t$ for $x \in[0,2]$. If $F^{\prime}(x)=f^{\prime}(x)$ for all $x \in(0,2)$, then $F(2)$ equals

Select the correct option:

A

$e^2-1$

B

$e^4-1$

C

$e-1$

D

$e^4$

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