Discovering the Integral

We are interested in finding an area under the curve. But this is really hard to do sometimes! Finding areas of rectangles is easy, though, so we can approximate the area under the curve with a rectangle. Move the points C and D to see how the area of the rectangle compares to the area underneath the curve.

The function A(x) represents the area under the curve between 0 and x. How can we use the function A(x) to find the area under the curve between C and D if C is not 0?

What happens to the area of the yellow rectangle and the blue area under the curve as delta gets smaller?

Betsy Vanfleet, 5 December 2013, Created with GeoGebra