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Home > AP Courses and Exams > Course Home Pages > Applications of the Definite Integral

Applications of the Definite Integral

Fun Finding Volume
"Did you ever think that finding the volume of a solid in a calculus class could be fun and tasteful?" asks this site, which helps teachers and students answer that question. It contains examples of the computation of volumes with the aid of oranges, apples, angel food cake, and muffins. The site features graphics, photographs, and the calculus computations involved in computing the volumes.
  Fun Finding Volume

Visualizations for Volumes of Solids in Calculus
This Web site is a comprehensive compilation of both static and animated graphics illustrating volumes of solids and the calculus involved in computing those volumes. The graphics are done quite well, and it is easy to view the relationship between the solids and the calculus method used to compute their volumes.
  Visualizations for Volumes of Solids in Calculus

Average Value of a Function
This brief tutorial discusses the method and formula for finding the Average Value of a Function and the Integral Form of the Mean Value Theorem. Applets discuss the derivations of the formulas. There are a few examples, including the average rate of change and the geometric interpretation of the theorem. This could serve as an introduction or a quick review of the topic for your class.
  Average Value of a Function

Arc Length
This brief tutorial discusses the formulas for finding the length of an arc in rectangular and parametric forms. Included is an applet showing the derivation of the formulas and a worked-out example for each. The page is part of Lawrence A. Husch's Visula Calculus site.
  Arc Length

Applications of Definite Integrals
This is part of a site maintained by Sandra Halfacre of White Station High School in Memphis, Tennessee. This particular page contains links to tutorials, slide shows, animations, and applets involving applications of the definite integral including net change, areas between curves, volumes, and arc length.
  Applications of Definite Integrals

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