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Did you know Sophia has tons of great content that aligns with the CCSS and NGSS standards? Get a jump on incorporating them into your everyday teaching.

Author:
Alex G

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.

Tutorial

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

Source: Self-created video

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

Source: Self-created video

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

Source: Self-created video

Source: Self-created video

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

Questions and Answers

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