Mathematics · 2021
JEE Main · 31 August 2021, Shift 2 · Q69
If [x] is the greatest integer ≤ x, then π^2 ∫_0^2( sin (π x)/2)(x-[x])^[x] d x is equal to:
If $\displaystyle [x]$ is the greatest integer $\displaystyle \leq x$, then $\displaystyle \pi^2 \int_0^2\left(\sin \frac{\pi x}{2}\right)(x-[x])^{[x]} \mathrm{d} x$ is equal to:
Official answer
(4)
$\displaystyle 4(\pi-1)$
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JEE Main 2021 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.