Let $ f $ be a continuous function satisfying $ \int_{0}^{t^{2}}\left(f(x)+x^{2}\right) \mathrm{dx}=\frac{4}{3} t^{3}, \forall t0 $. Then $ \mathrm{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) \mathrm{dx}=\frac{4}{3} t^{3}, \forall t>0 $. Then $ \mathrm{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) \mathrm{dx}=\frac{4}{3} t^{3}…

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