Answer
$$
\begin{aligned}
& F_R=107 \mathrm{kN} \\
& \bar{z}=2.40 \mathrm{~m}
\end{aligned}
$$
Work Step by Step
$$
\begin{aligned}
& \int d A=\int_0^4 4 z^{\frac{1}{2}} d z \\
& =\left[\frac{2}{3}(4) z^{\frac{1}{2}}\right]_0^4 \\
& =21.33 \mathrm{kN} / \mathrm{m} \\
& F_R=21.33(5)=107 \mathrm{kN} \\
& \int \bar{z} d A=\int_0^4 4 z^{\frac{1}{2}} d z \\
& =\left[\frac{2}{5}(4) z^{\frac{5}{2}}\right]_0^4 \\
& =51.2 \mathrm{kN} \\
& \bar{z}=\frac{51.2}{21.33}=2.40 \mathrm{~m} \\
&
\end{aligned}
$$
Also, from the back of the book,
$$
\begin{aligned}
A & =\frac{2}{3} a b=\frac{2}{3}(8)(4)=21.33 \\
F_R & =21.33(5)=107 \mathrm{kN} \\
\bar{z} & =4-1.6=2.40 \mathrm{~m}
\end{aligned}
$$
