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


Visualization:
Using Integral (from the University of Arizona):

  1. 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 .
  2. If you choose Yes then read the instructions and press when you are ready to proceed.
  3. Use the arrow keys to highlight Create Integrals and press .
  4. Use the arrow keys to highlight Create Integral and press .
  5. At the prompt, Enter integrand :, type
    3^x .
  6. At the prompt, Lower x limit : -10, type 0 .
  7. At the prompt, Upper x limit : 10, type 2 .
  8. Use the arrow keys to move to Plot Integrand (Rectangle) and press .
  9. At the prompt, Minimum y : -10, type 0 .
  10. At the prompt, Maximum y : 10, type 9 .
  11. 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.

  12. Press to clear the graph.
  13. Press uppercase several times until n = 200.
  14. Again, pressing yields that the value for the integral is 7.2806.
  15. Use the arrow keys to highlight Integral Operations and press .
  16. Use the arrow keys to highlight Arbitrary Point and press .
  17. As you keep pressing , you will see values of the Riemann sum using powers of 2 subintervals.