# Summation of Area ( Riemann Sums)

- Author:
- Dr. Doug Davis, 3D

- Topic:
- Area

Change the function by entering "f(x)= ____" in the Input bar.
The boundaries are currently fixed at 0 to 4 for cleaner screen.
Turning a checkbox on will show the corresponding Riemann Sum value and plot.
( Simpson's rule not shown on plot )
The number of subdivisions can be changed with the slider.

Change the number of intervals with the slider.
Show upper and lower sums. How do the sums vary as n increases?
Show the Left and Right sums. Are the Left and Right sums always between Upper and Lower sums?
HIde others and show left and trapezoid sums. Show Symbolic Integration for exact solution.
Which get closer to the exact solution, Trapezoid Sum or Left Sum?
Compare Midpoint sum, Trapezoid sum and Simpson's Rule for different n values?
Try the above with different functions?
Modified All Sums (Riemann Sums) from Ted Coe to add upper and lower sums.