∫−23|x−2|dx=∫−22|x−2|dx+∫23|x−2|dx =∫−22(2−x)dx+∫23(x−2)dx =(2x−x22)-22+(x22−2x)23 =172

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$\int_{- 2}^{3} | x - 2 | d x =$

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$\frac{7}{2}$

$\frac{17}{2}$

$\frac{5}{2}$

answer is D.

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Detailed Solution

$\int_{- 2}^{3} | x - 2 | d x = \int_{- 2}^{2} | x - 2 | d x + \int_{2}^{3} | x - 2 | d x$

$= \int_{- 2}^{2} (2 - x) d x + \int_{2}^{3} (x - 2) d x$

$= {(2 x - \frac{x^{2}}{2})}_{- 2}^{2} + {(\frac{x^{2}}{2} - 2 x)}_{2}^{3}$

$= \frac{17}{2}$

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