Problem:
Use the Midpoint Rule to approximate

with N rectangles where N = 10 and 50.


Visualization:
Using Microcalc:

  1. Choose Beginning Calculus from the initial menu and press .
  2. Use the arrow keys to move to the menu item Riemann Sums, press and .
  3. At the prompt F(x) =, enter the formula
    x^2+1
  4. Enter the bounds at the prompts
    x_0 = 0
    x_1 = 2
  5. Using the arrow keys, move to F(Midpoint) and press
  6. (*) At the prompt for the number of subdivisions, N = , enter 10
  7. You will see the the graph of the function and the approximating rectangles:

  8. Hitting , you will see the calculations up to that point.
  9. Hit , again and use the arrow keys to move to Change N Only and press .
  10. Return to (*) and enter N = 50 and proceed as above.

    You will see the following table at some point: