Problem:
Use the Midpoint Rule to approximate

with N rectangles where 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^2+1 .
  6. At the prompt, Lower x limit : -10, type .
  7. At the prompt, Upper x limit : 10, type .
  8. Use the arrow keys to move to Plot Integrand (Rectangle) and press .
  9. At the prompt, Minimum y : -10, type .
  10. At the prompt, Maximum y : 10, type .
  11. You will now see the graph of the function.
  12. Each time that you type uppercase the value of n will be increased by one and by typing lowercase you will decrease n by one. Proceed to make n=10.
  13. Press to pick the midpoint method and you get the following: