If $F\,\,\left( x \right) = \mathop \smallint \limits_{{x^2}}^{{x^3}} \,\,\log \,\,t\,\,dt\,\,(x > 0)$, then $F'\left( x \right)$ equals

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

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

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

, then

F'\left( x \right)

equals

View answer and explanation

Correct option: A

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

Option A is correct because the derivative of the integral is found using Leibniz's rule, resulting in (9x² - 4x)log x.

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