35-40 evaluate the integral by interpreting it in terms of areas. 39. \int_(-4)^(3)\left|(1)/(2) x\right| d x

asked Jun 28, 2023 48.3k views

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35-40 evaluate the integral by interpreting it in terms of areas.

39.
$\int_(-4)^(3)\left|(1)/(2) x\right| d x$

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The value of the definite integral corresponds to the total area of two triangles (see attached plot).

$\displaystyle \int_(-4)^3 \left|\frac x2\right| \, dx = \frac12 * 2 * 4 + \frac12 * 3 * \frac32 = \boxed{\frac{25}4}$

$35-40 evaluate the integral by interpreting it in terms of areas. 39. \int_(-4)^(3)\left-example-1$

Owen M answered Jul 2, 2023

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