Mathematics · 2021
JEE Main · 26 August 2021, Shift 2 · Q74
If the value of the integral ∫_0^5 (x+[x])/(e^x-[x]) d x=α e^-1+β, where α, β ∈ R, 5 α+6 β=0, and [x] denotes the greatest integer less than or equal…
If the value of the integral $\displaystyle \int_0^5 \frac{x+[x]}{\mathrm{e}^{x-[x]}} \mathrm{d} x=\alpha \mathrm{e}^{-1}+\beta$, where $\displaystyle \alpha, \beta \in \mathbf{R}, 5 \alpha+6 \beta=0$, and $\displaystyle [x]$ denotes the greatest integer less than or equal to $\displaystyle x$; then the value of $\displaystyle (\alpha+\beta)^2$ is equal to :
Official answer
(1)
$\displaystyle 25$
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JEE Main 2021 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.