Answer
81
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 $12\times 6$
* a right triangle with legs a=$6$, b=$3$
Total area = $12(6)$ + $\displaystyle \frac{1}{2}(6)(3)=72+9=81$
$\displaystyle \int_{0}^{12}f(x)dx=81$
