Problem:
Approximate the integral

by taking the average of the upper and lower Riemann sums with n=12.
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 Sum, press and .
  3. At the prompt F(x) =, enter the formula
    sin(x)
  4. Enter the bounds at the prompts
    x_0 = 0
    x_1 = pi
    You can enter pi by pressing at the same time.
  5. Use the arrow keys to move to the menu item Lower Riemann Sum, press .
  6. At the prompt, N = , enter 12 .
  7. You then see the following:

  8. Press and you will see the approximation using Lower Riemann Sums.
  9. Press again.
  10. Use the arrow keys to move to the menu item Upper Riemann Sum, press .
  11. At the prompt, N = , enter 12 .
  12. You then see the following:

  13. Press and you will see the following table: