Let $f:\left( {0,\,\,\infty } \right) \to R$ and $F\left( x \right) = \mathop \smallint \nolimits_0^x \,\,f\left( x \right)\,\,dt$. If $F\left( {{x^2}} \right) = {x^2}\left( {1 + x} \right)$, then $f\left( 4 \right)$ equals

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

Let

f:\left( {0,\,\,\infty } \right) \to R

and

F\left( x \right) = \int \nolimits_0^x \,\,f\left( x \right)\,\,dt

. If

F\left( {{x^2}} \right) = {x^2}\left( {1 + x} \right)

, then

f\left( 4 \right)

equals

View answer and explanation

Correct option: C

\mathrm{4}

Option C (4) is correct because differentiating F(x²) and solving for f(x) allows us to find f(4) = 4.

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