Areas Between Curves
In this lesson, we learn how to find the area between two curves using integration. We start with the familiar case of a region bounded by a non-negative function and the x-axis over an interval AB. We then move on to a more general case of a region bounded between two curves, where we approximate the region with rectangles and find the area differential dA equal to the difference of the two functions times dx. We then integrate dA to find the exact area between the two curves. The lesson includes examples of finding the area between curves by integrating with respect to both x and y.
How to find the area between two curves.
Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information on videos, resources, and lessons at http://online.math.uh.edu/HoustonACT/videocalculus/index.html.
- Some Area Problems - Some practice area problems.
- More on Area - More practice on area.
- How do you find the area between curves?
- How do you find the area of the region bounded by sin x and cos x?
- How do you find the area of the region bounded by y = x^2 and y = x + 2?
- How do you find the area between curves by using dy instead of dx?
- How do you set up an integral by using horizontal slices?
- How do you find the area of the region bounded by y = x^5 and y = x^2?
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Staff Review
The theory behind integrals and areas under curves is explained again, and this is applied to situations in which you would like to find the area between curves instead of the area under a curve. Several different example problems are done, showing how to think of the problems geometrically, how to set them up, and how to compute the areas. Some of the areas are able to be computed by splitting them up into multiple integrals, some are easier by integrating with respect to x, and some integrating with respect to y. A good variety of examples are provided. -
