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)?
![](../../mgifs/gifs3/area1.gif)
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:
![](../../mgifs/gifs3/area2.gif)
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
![](../../mgifs/gifs3/area5.gif)
3. Examples