Let f be a differentiable.... | JEE Advanced 2023 | Definite

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JEE Advance 2023

Paper-2 2023

Question

Let $f:[1, \infty) \rightarrow \mathbb{R}$ be a differentiable function such that $f(1)=\frac{1}{3}$ and $3 \int_1^x f(t) d t=x f(x)-\frac{x^3}{3}, x \in[1, \infty)$ Let $e$ denote the base of the natural logarithm. Then the value of f (e) is

Select the correct option:

A

$\frac{e^2+4}{3}$

B

$\frac{\log _e 4+e}{3}$

C

$\frac{4 e^2}{3}$

D

$\frac{e^2-4}{3}$

✓ Correct! Well done.

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