Obtain $\int_{1}^{e} (x^{2} - x) d x$ .

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Solution

$I = \int_{1}^{e} (x^{2} - x) d x$
$= {[\frac{x^{3}}{3} - \frac{x^{2}}{2}]}_{1}^{e}$
$= \frac{e^{3}}{3} - \frac{e^{2}}{2} + \frac{1}{6}$

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