Let [·] be the greatest integer... |JEE Main 2026 | Definite

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JEE MAIN 2026

22-01-2026 S2

Question

Let $[\cdot]$ be the greatest integer function. If $\alpha=\int_0^{64}\left(x^{1 / 3}-\left[x^{1 / 3}\right]\right) \mathrm{d} x$, then $\frac{1}{\pi} \int_0^{\alpha \pi}\left(\frac{\sin ^2 \theta}{\sin ^6 \theta+\cos ^6 \theta}\right) \mathrm{d} \theta$ is equal to $\_\_\_\_$ .

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