JEE Main 202122 Jul, Evening shiftMathematicsMediumIntegral Calculus369× since 2002If ∫0100πsin2xe(xπ−[xπ])dx=απ31+4π2,α∈R\int\limits_0^{100\pi } {{{{{\sin }^2}x} \over {{e^{\left( {{x \over \pi } - \left[ {{x \over \pi }} \right]} \right)}}}}dx = {{\alpha {\pi ^3}} \over {1 + 4{\pi ^2}}},\alpha \in R}0∫100πe(πx−[πx])sin2xdx=1+4π2απ3,α∈R where [x] is the greatest integer less than or equal to x, then the value of α\alphaα is :AOption A. 200 (1 −-− e^−-−1)BOption B. 100 (1 −-− e)COption C. 50 (e −-− 1)DOption D. 150 (e^−-−1 −-− 1)CheckSkip · show solution
