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Let f:[-(pi)/(2),(pi)/(2)]rarr R be a di...

Let `f:[-(pi)/(2),(pi)/(2)]rarr R` be a differentiable function such that `f(0)=(1)/(2)`.If the `lim_(x rarr0)(x int_(0)^(x)f(t)dt)/(e^(x^(2))-1)=alpha` then `8 alpha^(2)` is equal to:

A

16

B

1

C

2

D

4

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