The graph of g consists of two straight lines and a semicircle. Use it to eveluate the integral.12210203861.jpgint_10^30 g(x)dx

The integral ${\displaystyle {\int }_{10}^{30}g\left(x\right)dx}$ is the area between the graph of g and the horizontal x-axis on the interval ${\displaystyle 10\le x\le 30}$.
We note that this area forms a semicircle with radius r = 10. Since the semicricle lies below the horizontal axis, the integral will be negative.
The area of a circle is the product of ${\displaystyle \pi }$ and the squared radius ${\displaystyle r^2}$. The area of a semicircle is half the area of a circle.
${\displaystyle {\int }_{10}^{30}g\left(x\right)dx=-\frac{\pi r^2}{2}}$
${\displaystyle =-\frac{\pi \left({10}^2\right)}{2}}$
${\displaystyle =-\frac{100\pi }{2}}$
${\displaystyle =-50\pi }$
${\displaystyle \approx -157.0796}$