If $F\left( x \right) = \frac{1}{{{x^2}}}\,\,\mathop \smallint \limits_4^x \,\,\left[ {4{t^2}\,\, - \,\,2\,F'\,\,\left( t \right)} \right]\,dt$, then $F'\,\,\left( 4 \right)$ equals

${\rm{32}}\,{\rm{/}}\,{\rm{9}}$

${\rm{32}}\,{\rm{/}}\,{\rm{3}}$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Analyzing +4 | -1

F\left( x \right) = \frac{1}{{{x^2}}}\,\,\int \limits_4^x \,\,\left[ {4{t^2}\,\, - \,\,2\,F'\,\,\left( t \right)} \right]\,dt

, then

F'\,\,\left( 4 \right)

equals

View answer and explanation

Correct option: C

\mathrm{32}\,\mathrm{/}\,\mathrm{9}

Option C (

\frac{\mathrm{32}}{\mathrm{9}}

) is correct because after differentiating and substituting, the value of

F'(4)

is found to be

\frac{\mathrm{32}}{\mathrm{9}}

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