Let f be a continuous function satisfying ∫₀ᵗ²... | Integrals

JEE MAIN 2023

10-4-2023 S2

Question

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

Select the correct option:

$\pi\left(1-\frac{\pi^3}{16}\right)$

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

$-\pi\left(1+\frac{\pi^3}{16}\right)$

$\pi^2\left(1-\frac{\pi^3}{16}\right)$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

Question Tags

JEE Main

Mathematics

Easy

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