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Definite Integration question

2010 · Shift 2 · Q31

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PYQ Library
JEE Advanced
Mathematics
Definite Integration
2010 · Shift 2 · Q31

Definite Integration question

2010 · Shift 2 · Q31

JEE AdvancedMathematicsDefinite IntegrationMCQ+4 / −1

Let

f

be a real-valued function defined on the interval

(-1, 1)

such that

{e^{ - x}}f\left( x \right) = 2 + \int\limits_0^x {\sqrt {{t^4} + 1} \,\,dt,}

for all

x \in \left( { - 1,1} \right)

, and let

{f^{ - 1}}

be the inverse function of

f

. Then

\left( {{f^{ - 1}}} \right)'\left( 2 \right)

is equal to

A
$1$
B
${{1 \over 3}}$
C
${{1 \over 2}}$
D
${{1 \over e}}$

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