Aim of the applet

Interpret geometrically the upper and lower Riemann sum.

Input data

• The function f(x).
• The interval [A,B] where the sums are calculated and modify dragging points A and B on the axis OX.
• The number of partitions is modified by dragging the point n.

Output data

• Upper Riemann sum: red.
• Lower Riemann sum: blue.

First steps

• Given the function f (x) = x ^ 2-3x calculates the upper and lower sums in the interval [-2.3] for n=4. Increases n = 7 and analyzed the behavior of Riemann sums when you refine the partition.
• Calculates Riemann sum for f (x) = cos x on [0,1] n = 10. If you increases n to 200, the lower and upper sum are nearest, among them is the value of the definite integral. Is the area under the graph of f on [0,1]? Change the interval for other situations.
• Write any function and calculates Riemann sum. Slide n, what are the highest and lowest sums that you can get?