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Definite Integration question

2021 · 22 Jul · Shift 2 · Q28

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PYQ Library
JEE Main
Mathematics
Definite Integration
2021 · 22 Jul · Shift 2 · Q28

Definite Integration question

2021 · 22 Jul · Shift 2 · Q28

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

If

\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}

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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