Problem:
Using the TI-85 graphing calculator, approximate the value of using the Trapezoidal Rule with a partition of 100 points.

Visualization: [Press here to see animation again!]

1. We enter the function on the calculator: 2. Subdivide [1,3] into 100 subintervals of equal length.
3. The length of each of these subintervals is which is (3 - 1))/100 = 1/50.
4. We determine the endpoints of these subintervals:

ai = 1 + i (1/50) = 1 + i/50

5. We enter the left-hand endpoints on the calculator and store them in the variable x: 6. The calculator displays the list of left-hand endpoints: 7. The calculator automatically stores the values of f(ai) in the list y1.
8. We now take the sum of the list y1, multiply by delta x, and store the answer in the variable L: 9. We enter the right-hand endpoints on the calculator and store them in the variable x: 10. The calculator displays the list of left-hand endpoints: 11. Again, the calculator automatically stores the values of f(ai) in the list y1.
12. We now take the sum of the list y1, multiply by delta x, and store the answer in the variable R: 13. Finally, we take the average of the sums: 