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AP Calculus AB: Area and Volume Concepts

AP Calculus AB: Area and Volume Concepts

 
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Author: Alex G
Objective:

Students should be able to understand the concepts of calculating the area between two curves, either in terms of x or in terms of y.

Students should be able to calculate the volume of a solid generated by revolving a region about the x axis using washers.

Students should be able to calculate the volume of a solid generated by revolving a region about a horizontal line that is not an axis and is either above or below the curve.

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Tutorial

Area Between Two Curves

How to Calculate the area of the region enclosed between two curves.

Source: Self-created video

Questions Like These

Using information from this video, you should be able to solve problem 1A from the AP College Board's released 2010 Form B exam

Source: AP College Board

Volume of revolution about x-axis (using washers)

Source: Self-created video

Questions Like These

Using information from this video, you should be able to solve Question 1B from the AP College Board's released 2007 Exam.

(Note, however, that seeing the full graph for this region on your calculator requires you change the window size. Viewing the graph in a standard window makes it appear to have a vertical asymptote at x = 0. It does not.)

Source: AP College Board

Revolving about a horizontal line above your region

Source: Self-created video

Revolving about a horizontal line below your region

Source: Self-created video

Questions Like These

Using the information from the two previous videos, you should be able to answer Question 1B on the College Board's released 2010 Form B Exam.

Source: AP College Board

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