Examine areas as integrals and as rectangles for given functions.

• Examine areas as integrals and as rectangles for given functions in order to determine the properties of functions that allow the areas to be equal

Students will find a rectangle whose area is the same as the area under a curve within a defined interval. Students will examine several examples and then try to generalize conditions that allowed the area of the rectangle and the area under the curve to be equal, leading to the Mean Value Theorem for Integrals.