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3D Integration Procedure

# 3D Integration Procedure - The Procedure for...

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G ( u , v ) du dv u i u f ! v i v f ! G ( u ) du u i u f ! G ( u , v , w ) du u i u f ! dvdw v i v f ! w i w f ! The Procedure for Multidimensional Integration Definition of they key word “ PARAMETRIZE ” as used below: Express all quantities that vary over the integral entirely in terms of your integration parameters ( IP s) and constants. 1. Parametrize the Region n ( n =1,2,3 n = path,surface,volume) a. Pick your coordinate system r i = ( x , y , z ) Cartesian, or ( r , θ , φ ) spherical, or ( s , , z ) cylind. b. Pick your n integration parameters u j . These n IPs will sweep out the n -dimensional region n in your integral. If possible, use one of more of your chosen coordinates r i . c. Describe the shape of by expressing your coordinates r i as functions 1 r i ( u j ) of the IPs d. Describe the edges of by providing bounds on each integration parameter u j 2. Parametrize the Differential d n using your coordinate system’s Line Element d ! l

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3D Integration Procedure - The Procedure for...

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