Using Riemann sums, give graphical and numerical evidence for the value of the integral

Using Integral (from the University of Arizona):

- After starting up the program, you are prompted
*"Would you like some instructions?"*Use the arrow keys to move to either*Yes*or*No*and then press . - If you choose
*Yes*then read the instructions and press when you are ready to proceed. - Use the arrow keys to highlight
*Create Integrals*and press . - Use the arrow keys to highlight
*Create Integral*and press . - At the prompt,
*Enter integrand :*, type3^x . - At the prompt,
*Lower x limit : -10*, type 0 . - At the prompt,
*Upper x limit : 10*, type 2 . - Use the arrow keys to move to
*Plot Integrand (Rectangle)*and press . - At the prompt,
*Minimum y : -10*, type 0 . - At the prompt,
*Maximum y : 10*, type 9 . - You will now see the graph of the function. Press
for
*Arbitrary*which means that each of the points from each of the subintervals is chosen randomly. - Press to clear the graph.
- Press uppercase
several times until
*n = 200*. - Again, pressing yields that the value for the integral is 7.2806.
- Use the arrow keys to highlight
*Integral Operations*and press . - Use the arrow keys to highlight
*Arbitrary Point*and press . - As you keep pressing , you will
see values of the Riemann sum using powers of 2 subintervals.