An applet that enables the user to investigate upper and lower sums as a method for finding the area under a curve. [br][br]Enter a function in the input box located in the top right corner. Move points A and B in the graph on the left to designate the start and end values for the sums. Use the slider for n to adjust the number of rectangles. Switch between the lower sum, upper sum, and area under the curve by clicking on the checkboxes. As you explore, compare the values of the upper and lower sums to the area under the curve. Under what conditions, do the upper and lower sums adequately approximate the area under the curve? [br][br]Based on your findings, what happens as the number of rectangles approaches infinity?