JEE Main 202622 Jan, Evening shiftMathematicsMediumIntegral Calculus369× since 2002Let [⋅][\cdot][⋅] be the greatest integer function. If α=∫064(x1/3−[x1/3])dx\alpha=\int_0^{64}\left(x^{1/3}-[x^{1/3}]\right)dxα=∫064(x1/3−[x1/3])dx, then 1π∫0απ(sin2θsin6θ+cos6θ)dθ\frac{1}{\pi}\int_0^{\alpha\pi}\left(\frac{\sin^2\theta}{\sin^6\theta+\cos^6\theta}\right)d\thetaπ1∫0απ(sin6θ+cos6θsin2θ)dθ is equal to ________.Your answerType your answer. Integers and decimals are accepted.CheckSkip · show solution
