(Solved): The continuous function f is defined on the interval [3,10]. The graph on the interval [2,8] is ...

The continuous function $f$ is defined on the interval $[-3,10]$. The graph on the interval $[2,8]$ is a semicircle. The figure above shows a portion of the graph of $f$. The graph contains the point $(3,\sqrt{5})$ and crosses the $x$-axis at the point $\left(-\frac{3}{2},0\right)$. (a) If ${\int }_0^{10}f(x)dx=20$, what is the value of ${\int }_8^{10}f(x)dx$ ? (b) Evaluate ${\int }_2^{3}4f^{\prime }(x)dx$ (c) Evaluate ${\lim }_{x\to -1}\frac{3f(x)-3}{2(x+1)}$.