If $F\left( x \right) = \mathop \smallint \nolimits_{{x^2}}^{{x^3}} \,\,\log \,\,t\,dt,\;\,\left( {x > 0} \right)$, then $F'\,\left( x \right)$ is equal to

$\left( {4x\,\, - \,\,9{x^2}} \right)\log \,\,x$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

F\left( x \right) = \int \nolimits_{{x^2}}^{{x^3}} \,\,\log \,\,t\,dt,\;\,\left( {x > 0} \right)

, then

F'\,\left( x \right)

is equal to

View answer and explanation

Correct option: A

\left( {9{x^2} - \,\,4x} \right)\,\,\log \,\,x

Option A (

\left( {9{x^2} - \,4x} \right)\,\,\log \,x

) is correct because it is the result of applying Leibniz's rule for differentiation under the integral sign.

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