The graph of g consists of two straight lines and a semicircle. Use it to...

The integral ${\displaystyle {\int }_0^{35}g\left(x\right)dx}$ is the area between the graph of g and the horizontal x-axis on the interval ${\displaystyle 0\le x\le 35}$. We separate this integral into the parts of (a) and (b) along with
${\displaystyle {\int }_{30}^{35}g\left(x\right)dx}$.
${\displaystyle {\int }_{30}^{35}g\left(x\right)dx}$ represents the area that forms a triangle with base b = 5 and height h = 5.
The area of a triangle is the product of the base b and the height h, divided by 2.
${\displaystyle {\int }_{30}^{35}g\left(x\right)dx=\frac{b\cdot h}{2}}$
${\displaystyle =\frac{5\cdot 5}{2}}$
${\displaystyle =\frac{25}{2}}$
=12.5