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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

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

C

`50 (e - 1)`

D

`100 (1-e)`

Text Solution

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The correct Answer is:
A
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