Consider the function $f(x) = \sin(\frac{\pi x}{18})$.
A. Using five subintervals and rectangles, taking the sample points to be left endpoints of the subintervals, approximate (to six decimal places) the area under the graph of $f(x)$ over the interval $[0, 9]$. (On paper, write the mathematical expression that you used to find the approximation. Be sure to check your calculator MODE.)
Area under the graph $\approx$
B. Repeat part A, but now using 50 subintervals. Use appropriate technology, noting any important values you needed to find the approximation.
Area under the graph $\approx$
C. Repeat part A, but now using 100 subintervals. Use appropriate technology, noting any important values you needed to find the approximation.
Area under the graph $\approx$
D. Now, write an expression (not a number) that represents the exact area under the graph of $f(x)$ over the interval $[0, 9]$. (Note that you can use the $\sum$ button in the editor to add math symbols.)
Area under the graph =
E. Use calculus (showing the appropriate work on paper) to calculate the exact area under the graph of $f(x)$ over the interval $[0, 9]$.
Area under the graph =
