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By using the properties of definite integrals, evaluate the integrals
$\int_{-5}^5|x+2| d x=I(s a y)$
$\int_{-5}^5|x+2| d x=I(s a y)$
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$\mathrm{I}=\int_{-5}^{-2}|\mathrm{x}+2| \mathrm{dx}\left|+\int_{-2}^5\right| \mathrm{x}+2 \mid \mathrm{dx}$
at $\mathrm{x}=-5, \mathrm{x}+2 < 0$; at $\mathrm{x}=-2, \mathrm{x}+2=0$; at $\mathrm{x}=5$, $x+2>0 ; x+2 < 0, \quad x+2=0, \quad x+2>0$
$I=-\int_{-5}^{-2} x+2 d x+\int_{-2}^5 x+2 d x$
$=-\left[\frac{x^2}{2}+2 x\right]_{-5}^{-2}+\left[\frac{x^2}{2}+2 x\right]_{-2}^5=29$
at $\mathrm{x}=-5, \mathrm{x}+2 < 0$; at $\mathrm{x}=-2, \mathrm{x}+2=0$; at $\mathrm{x}=5$, $x+2>0 ; x+2 < 0, \quad x+2=0, \quad x+2>0$
$I=-\int_{-5}^{-2} x+2 d x+\int_{-2}^5 x+2 d x$
$=-\left[\frac{x^2}{2}+2 x\right]_{-5}^{-2}+\left[\frac{x^2}{2}+2 x\right]_{-2}^5=29$
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