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If ∫\limits_0^100π \sin ^2x \over e^\left( x \over π - \left[ x \over π \right] \right)dx = α π ^3 \over 1 + 4π ^2,α \in R where [x] is the greatest integer less than or equal to x, then the value of α is : | Watch the step-by-step video solution for this NIMCET PYQ.