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If int(0)^(100pi)(sin^(2)x)/(e^(((x)/(pi...

If `int_(0)^(100pi)(sin^(2)x)/(e^(((x)/(pi)-[(x)/(pi)]))) dx = (alpha pi^(3))/(1 + 4pi^(2)), alpha in R` where [x] is the greatest integer less than or equal to x, then the value of `alpha` is :

A

`200 (1-e^(-1))`

B

`100(1-e)`

C

`50 (e-1)`

D

`150(e^(-1)-1)`

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