Let $f:(0, \infty) \rightarrow \mathbf{R}$ and let $F(x)=\int_\limits 0^x f(t) d t$ If $F\left(x^2\right)=x^2(1+x)$, then $f(4)$ equals

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

Let

f:(0, \infty) \rightarrow \mathbf{R}

and let

F(x)=\int\limits_{0}^x f(t) d t

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

, then

f(4)

equals

View answer and explanation

Correct option: C

Option C (4) is correct because by using the fundamental theorem of calculus and differentiating the given equation, we can find f(4).

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