Lesson 17 - Volume by Integration

# Lesson 17 - Volume by Integration - TOPIC APPLICATIONS...

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TOPIC APPLICATIONS VOLUME BY INTEGRATION

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define what a solid of revolution is decide which method will best determine the volume of the solid apply the different integration formulas. OBJECTIVES
DEFINITION A solid of revolution is the figure formed when a plane region is revolved about a fixed line. The fixed line is called the axis of revolution . For short, we shall refer to the fixed line as axis . The volume of a solid of revolution may be using the following methods: DISK, RING and SHELL METHOD

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This method is used when the element (representative strip) is perpendicular to and touching the axis. Meaning, the axis is part of the boundary of the plane area. When the strip is revolved about the axis of rotation a DISK is generated. A. DISK METHOD: V = π r 2 h
h = dx y dx x = a f(x) - 0 x = b y = f(x) x = r The solid formed by revolving the strip is a cylinder whose volume is h r V 2 π = [ ] dx x f V 2 0 ) ( - = π To find the volume of the entire solid [ ] = b a dx x f V 2 ) (

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Volume by disks
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## This note was uploaded on 10/19/2011 for the course MATH 22 taught by Professor Ma'amzapanta during the Fall '11 term at Mapúa Institute of Technology.

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Lesson 17 - Volume by Integration - TOPIC APPLICATIONS...

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