JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

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Analyzing +4 | -1

\int\limits_0^{100\,\pi } {\frac{{{{\sin }^2}x}}{{{e^{\left( {\frac{x}{\pi } - \left[ {\frac{x}{\pi }} \right]} \right)}}}}} \,dx = \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

View answer and explanation

Correct option: A

200\,(1 - {e^{ - 1}})

Option A (

200\,(1 - {e^{ - 1}})

) is correct because the integral can be simplified using the periodicity of the sine function and then evaluated, leading to the given result.

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