Problem:
Approximate the integral

by taking the average of the upper and lower Riemann sums with n=12.

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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: