Lesson #108
Area Between Two Curves

Quote of the Day:
"With an absurd oversimplification, the "invention" of the calculus is sometimes ascribed to two men, Newton and Leibniz. In reality, the calculus is the product of a long evolution that was neither initiated nor terminated by Newton and Leibniz, but in which both played a decisive part." -- Richard Courant and Herbert Robbins

Objectives:
The student will compute the area between 2 curves.

1. Introduction:

How would you determine the area between two curves (i.e., how would you find the shaded area in the figures below)?



Area can be found by finding the area under the "top" curve and subtracting the area under the "bottom" curve. Look at the example below:



Note that the area could be summed up by taking areas of rectangles and then applying a limit (you can see a few representative rectangles drawn in the third figure). The rectangles are drawn vertically (this is important -- as you will see in tomorrow's lesson).

2. Example









3. Examples

4. Assignment:
p. 448 (1, 2, 5a, 7, 8)

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Send any comments or questions to: David Pleacher