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Definite Integration question

2022 · 27 Jun · Shift 2 · Q26

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PYQ Library
JEE Main
Mathematics
Definite Integration
2022 · 27 Jun · Shift 2 · Q26

Definite Integration question

2022 · 27 Jun · Shift 2 · Q26

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

Let f be a differentiable function in

\left( {0,{\pi \over 2}} \right)

. If

\int\limits_{\cos x}^1 {{t^2}\,f(t)dt = {{\sin }^3}x + \cos x}

, then

{1 \over {\sqrt 3 }}f'\left( {{1 \over {\sqrt 3 }}} \right)

is equal to

A
$6 - 9\sqrt 2$
B
$6 - {9 \over {\sqrt 2 }}$
C
${9 \over 2} - 6\sqrt 2$
D
${9 \over {\sqrt 2 }} - 6$

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