Mathematics · 2023
JEE Main · 10 April 2023, Shift 2 · Q11
Let f be a continuous function satisfying ∫_0^t^2(f(x)+x^2) d x=4/3 t^3, ∀ t>0. Then f((π^2)/4) is equal to
Let $\displaystyle f$ be a continuous function satisfying $\displaystyle \int_0^{t^2}\left(f(x)+x^2\right) d x=\frac{4}{3} t^3, \forall t>0$. Then $\displaystyle f\left(\frac{\pi^2}{4}\right)$ is equal to
Official answer
From NTA’s final answer key for this paper.
(4)
$\displaystyle \pi\left(1-\frac{\pi^3}{16}\right)$
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JEE Main 2023 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.