First slide

Evaluation of definite integrals

Question

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

Easy

A

0
B

$\frac{5}{2}$
C

$\frac{7}{2}$
D

$\frac{17}{2}$

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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