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

Question

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

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

Answer 1

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}`