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Applications of integration

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This document discusses methods for calculating volumes using integration. There are three main methods - disc, washer, and shell. The disc and washer methods use the formula πr2h to find the volume of revolution around an axis, with disc used for hollow shapes and washer for shapes within other shapes. The shell method uses 2πrh and is primarily used for revolutions around the y-axis. It is important to determine the correct graph and limits of integration based on the problem.

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Applications of IntegrationVolume Methods
VariablesIntegral- area which is being found for area/volume, dictated by two points on a graph from point A to BF(x)=a,bRevolve around the X-axis or Y-Axis
EquationsVdisc/washer= ∏r2 hVshell= 2 ∏rh
MethodsDisc Method - Disc method is used with hollow solids when finding volume-top-bottom - be sure to determinewhich graph is on top and which is on thebottom
Washer Methodis used when there are two solids within each otherSame equation as disc methodTop-bottom
Shell MethodUsed primarily when it is on the y-axis Different equation than disc and washerCan be used at any timeRemember! When rotated aroundthe x-axis the equation should be in terms of y.
Remember!To change the equation if on the y-axis
Remember!You can determine which graph is on top and which is on the bottom by plugging in a number which is in the interval and the bigger of the two is the one on top
Practice X2-9=f(x) 1) Graph the function 2) Find the Interval (-3,3) 3) Set Up the Integral∏∫ X2-9 (a,b = -3,3) 4) Solve using Calculator 5) Don’t forget units

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Applications of integration