Answer
$\int_{0}^{8}sin~\sqrt{x}~dx \approx 6.1820$
Work Step by Step
$\Delta x = \frac{b-a}{n} = \frac{8-0}{4} = 2$
We can find the midpoints of the four subintervals:
$x_1 = 1$
$x_2 = 3$
$x_3 = 5$
$x_4 = 7$
$\int_{0}^{8}sin~\sqrt{x}~dx \approx \sum_{i=1}^{4} f(x_i)~\Delta x$
$\int_{0}^{8}sin~\sqrt{x}~dx \approx 2\cdot (sin~\sqrt{1}+sin~\sqrt{3}+sin~\sqrt{5}+sin~\sqrt{7})$
$\int_{0}^{8}sin~\sqrt{x}~dx \approx 2\cdot (3.09102)$
$\int_{0}^{8}sin~\sqrt{x}~dx \approx 6.1820$
