Answer
40
Work Step by Step
Graphing the function,
(On desmos.com the syntax for a piecewise function is:
f(x)=$\{$condition:expression, condition: expression, etc.$\}$ )
we see that the area beneath the graph consists of
* a rectangle with sides 8$\times$4
* a right triangle with legs a=4, b=4
Total area = $8(4)$ + $\displaystyle \frac{1}{2}(4)(4)=32+8=40$
$\displaystyle \int_{0}^{8}f(x)dx=40$
