module1_MAT-232-jan12 - MAT232:CALCULUSII TOPICS (

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MAT­232: CALCULUS II Module 1—Applications of Integration TOPICS Module 1 covers the following topics: determining the volume of various geometric objects by applying the definition of the definite integral choosing the most appropriate method for finding the volume of a solid of revolution (disc, washer, shell, or cross sections) recognizing which variable represents the radius, the height, and the thickness of the differential object when a strip is revolved about an axis expressing x as a function of y , when appropriate, given y = f ( x ) STUDY MATERIALS Textbook Readings Study sections 5.2, 5.3, and 5.4 in the course textbook. Then read the Technical Commentary topics given below. Technical Commentary Read the following brief commentary topics for further explanations and notes on the material covered in this module. Following the commentary are video tutorials and suggested Self­Check Exercises. Be sure to work through these practice exercises to help solidify the skills learned in the module and to prepare for the module­ending written assignment. The Disk Method The Washer Method The Shell Method Arc Length Video Tutorials Introduction to Definite Integrals (YouTube video, 9:18 min.), KhanAcademy (), Solid of Revolution: Copyright © 2012 by Thomas Edison State College. All rights reserved.
Solid of Revolution (Part 1) —Figuring out the volume of a function rotated about the x ­axis (YouTube video, 10:04 min.), KhanAcademy (), Solid of Revolution (Part 2) —The volume of y = sqrt( x ) between x = 0 and x = 1 rotated around x ­axis (YouTube video, 7:31 min.), KhanAcademy (), Solid of Revolution (Part 3) —Figuring out the equation for the volume of a sphere (YouTube video, 8:58 min.), KhanAcademy (),

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