# Evaluate each definite integral. int_3^0(x+2)dx

Evaluate each definite integral.
${\int }_{3}^{0}\left(x+2\right)dx$
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Evaluating ${\int }_{3}^{0}\left(x+2\right)dx$,
${\int }_{3}^{0}\left(x+2\right)dx=-{\int }_{0}^{3}\left(x+2\right)dx$
$\left[\because {\int }_{a}^{b}f\left(x\right)dx=-{\int }_{b}^{a}f\left(x\right)dx\right]$
$⇒{\int }_{3}^{0}\left(x+2\right)dx=-{\left[\frac{{x}^{2}}{2}+2x\right]}_{0}^{3}$

$⇒{\int }_{3}^{0}\left(x+2\right)dx=-\left(\frac{{3}^{2}}{2}+2×3\right)+\left(\frac{{0}^{2}}{2}+2×0\right)$
$⇒{\int }_{3}^{0}\left(x+2\right)dx=-\left(\frac{21}{2}\right)$
Result:${\int }_{3}^{0}\left(x+2\right)dx=-\left(\frac{21}{2}\right)=-10.5$

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