Answer
$$
\int_{0}^{8} \sin \sqrt{x} d x, \quad n=4
$$
The Midpoint Rule gives
$$
\begin{aligned}
\int_{0}^{8} \sin \sqrt{x} d x \approx \sum_{i=1}^{4} f\left(\bar{x}_{i}\right) \Delta x \approx 2(3.0910)=6.1820
\end{aligned}
$$
Work Step by Step
$$
\int_{0}^{8} \sin \sqrt{x} d x, \quad n=4
$$
The width of the subintervals is
$$
\Delta x=(8-0) / 4=2,
$$
so the endpoints are 0,2,4,6, and 8, and the midpoints are 1,3,5, and 7.
The Midpoint Rule gives
$$
\begin{aligned}
\int_{0}^{8} \sin \sqrt{x} d x \approx \sum_{i=1}^{4} f\left(\bar{x}_{i}\right) \Delta x \\
& =2(\sin \sqrt{1}+\sin \sqrt{3}+\sin \sqrt{5}+\sin \sqrt{7}) \\
& \approx 2(3.0910)=6.1820
\end{aligned}
$$
