Problem:
Use Riemann sums to approximate the area bounded by the graph of

f(x) = x3 - 5x +7

the lines x = -2 and x = 3 and the x-axis. Use N left-hand endpoints for N = 10 and 50.

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
    x^3-5*x+7 .
  6. At the prompt, Lower x limit : -10, type -2 .
  7. At the prompt, Upper x limit : 10, type 3 .
  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 20 .
  11. You will now see the graph of the function. Press uppercase several times until n = 10. Note that the value of n is at the upper left-hand side of the screen.
  12. Now press to choose left-hand endpoints:

  13. Press to clear the graph.
  14. Again press uppercase several times until n = 50.
  15. Finally, press to choose left-hand endpoints.