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Differentiation question

2014 · Shift 2 · Q34

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PYQ Library
JEE Advanced
Mathematics
Differentiation
2014 · Shift 2 · Q34

Differentiation question

2014 · Shift 2 · Q34

JEE AdvancedMathematicsDifferentiationMCQ+3 / −1

Let

f:\left[ {0,2} \right] \to R

be a function which is continuous on

\left[ {0,2} \right]

and is differentiable on

(0,2)

with

f(0)=1

. Let

F\left( x \right) = \int\limits_0^{{x^2}} {f\left( {\sqrt t } \right)dt}

for

x \in \left[ {0,2} \right]

. If

F'\left( x \right) = f'\left( x \right)

for all

x \in \left[ {0,2} \right]

, then

F(2)

equals

A
${e^2} - 1$
B
${e^4} - 1$
C
$e - 1$
D
${e^4}$

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