We will look at a way to find the area under a curve. One way to do this is to divide the area into rectangles. You can investigate different functions and move the slider for n to change the number of rectangles. We will look at two ways of getting our rectangles, upper rectangles and lower rectangles. You can move points A and B along the x-axis to change the boundaries for the interval.

What happens to the value of the upper and lower sums as you increase the number of rectangles?[br]As the number of rectangles increases, does the estimate get closer to the actual value?[br]As the number of rectangles for the Uppersum increases, the area estimate decreases. Will it continue to decrease as the number of rectangles goes towards infinity?[br]Is there another way you could get the heights of rectangles other than Upper or Lower sums?[br]Are there any other shapes you could divide the area under the curve into?