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AP Calculus AB/BC Area & Volume

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Page 1: Area and Volumes of Revolution

AP Calculus AB/BC

Area & Volume

Page 2: Area and Volumes of Revolution

Area & Volume

• Larson 6.1, 6.2, 6.3, FDWK 7.2, 7.3• Area Between Two Curves• Area Between Intersecting Curves• Area With Respect to • Volumes of Revolution – Disks• Volumes of Revolution – Washers• Volumes of Revolution – Cylindrical Shells• Solids With Known Cross-Sections

Page 3: Area and Volumes of Revolution

Area Between Two Curves

Page 4: Area and Volumes of Revolution

Example 1

Sketch the region bounded by the graphs of the algebraic functions

and find the area of the region.

Page 5: Area and Volumes of Revolution

Click here for video

http://screencast.com/t/jTL7JAs9Y
Page 6: Area and Volumes of Revolution

Example 2

Sketch the region bounded by the graphs of the algebraic functions

and find the area of the region.

Page 7: Area and Volumes of Revolution

Click here for video

http://screencast.com/t/GT5CjXP92j
Page 8: Area and Volumes of Revolution

Example 3

Find the area enclosed between the graphs of

Page 9: Area and Volumes of Revolution

Click here for 1st video Click here for 2nd video

http://screencast.com/t/zIcVfRyv
http://screencast.com/t/zIcVfRyv
http://screencast.com/t/zIcVfRyv
http://screencast.com/t/3QdptbrX7jaT
http://screencast.com/t/3QdptbrX7jaT
http://screencast.com/t/3QdptbrX7jaT
Page 10: Area and Volumes of Revolution

Click here for video

http://screencast.com/t/jCxoFKJw7Q
Page 11: Area and Volumes of Revolution

Example 4

Find the volume of the solid formed by revolving the region bounded by the -axis, the graph of and the line about the -axis.

Page 12: Area and Volumes of Revolution

Click here for video

http://screencast.com/t/XbQEByxd1cwt
Page 13: Area and Volumes of Revolution

Example 5

Find the volume of the solid formed by revolving the region bounded by the graphs of and about the -axis.

Page 14: Area and Volumes of Revolution

Click here for video

http://screencast.com/t/IRffFzuc3P9

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AB Calculus - Hardtke Assignment 6.2: Volumes of ...faculty.muhs.edu/hardtke/ABCalc_Notes2012-13/Assignment 6.2 Volume by... · Assignment 6.2: Volumes of Revolution Name_____ Due

SECTION 6.2: VOLUMES OF SOLIDS OF …Section 6.2: Volumes of Solids of Revolution: Disk / Washer Methods) 6.2.2 It helps that the axis of revolution does not pass through the interior

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