Mathematics · 2021
JEE Main · 22 July 2021, Shift 2 · Q76
If ∫_0^100 π (sin^2 x)/(e^(x/(π)-[x/(π)])) d x=(α π^3)/(1+4 π^2), α ∈ R, where [x] is the greatest integer less than or equal to x, then the value of…
If $\displaystyle \int_0^{100 \pi} \frac{\sin ^2 x}{e^{\left(\frac{x}{\pi}-\left[\frac{x}{\pi}\right]\right)}} \mathrm{d} x=\frac{\alpha \pi^3}{1+4 \pi^2}, \alpha \in \mathbf{R}$,
where $\displaystyle [x]$ is the greatest integer less than or equal to $\displaystyle x$, then the value of $\displaystyle \alpha$ is :
Official answer
(4)
$\displaystyle 200\left(1-\mathrm{e}^{-1}\right)$
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JEE Main 2021 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.