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For real $\alpha$, the value of $\int_{\alpha}^{\alpha+1} [x]dx$, where $[x]$ denotes the largest integer less than or equal to $x$, is

  1. $\alpha$
  2. $[\alpha]$
  3. $1$
  4. $\dfrac{[\alpha] + [\alpha +1]}{2}$
in Calculus by Veteran (431k points)
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