If ∫₀^{100π} sin²x / e^(x/π − [x/π]) dx

_JEE MAIN_2021_

22-JULY-2021,S2

Question

If $\int_0^{100 \pi} \frac{\sin ^2 x}{e^{\left(\frac{x}{\pi}-\left[\frac{x}{\pi}\right]\right)}} d x=\frac{\alpha \pi^3}{1+4 \pi^2}, \alpha \in R$ where $[x]$ is the greatest integer less than or equal to $x$, then the value of $\alpha$ is:

Select the correct option:

$200\left(1-e^{-1}\right)$

$200(1-e)$

$50(e-1)$

$150\left(e^{-1}-1\right)$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

Question Tags

JEE Main

Mathematics

Hard

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