Let $f$ be a continuous function satisfying $\int_0^{t^2}\left(f(x)+x^2\right) d x=\frac{4}{3} t^3, \forall t0$. Then $f\left(\frac{\pi^2}{4}\right)$ is equal to: [JEE Main 2023, 10 Apr (Shift 2)]

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: [JEE Main 2023, 10 Apr (Shift 2)]

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Let \(f\) be a continuous function satisfying \(\int_0^{t^2}\left(f(x)+x^2\right) d x=\frac{4}{3} t^3, \forall t>0\).…

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Let \(f\) be a continuous function satisfying \(\int_0^{t^2}\left(f(x)+x^2\right) d x=\frac{4}{3} t^3, \forall t&gt;0\).…

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Let \(f\) be a continuous function satisfying \(\int_0^{t^2}\left(f(x)+x^2\right) d x=\frac{4}{3} t^3, \forall t>0\).…