Let f be a continuous function satisfying ∫₀^t² ( f(x) + x²) dx =… | JEE Main 2023 Mathematics PYQ

MCQMediumJEE Main 2023 · 10 April, Shift 2Definite Integrals

Let $f$ be a continuous function satisfying $\int_0^{t^2} \left( f(x) + x^2 \right) \, dx = \frac{4}{3} t^3$ , $\forall t > 0$ . Then $f \left( \frac{\pi^2}{4} \right)$ is equal to:

A
$-\pi^2 \left( 1 + \frac{\pi^2}{16} \right)$
B
$\pi \left( 1 - \frac{\pi^3}{16} \right)$
C
$-\pi \left( 1 + \frac{\pi^3}{16} \right)$
D
$\pi^2 \left( 1 - \frac{\pi^3}{16} \right)$

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