Lectures32and33

Lectures32and33 - F ig e : i e eg a f ed ed h e eced igd ic...

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Unformatted text preview: F ig e : i e eg a f ed ed h e eced igd ic i h e h ec ce fa i e i eg a h db eaa a e e i fh ec ce f ig e i eg a ad db e i eg a e i b e eak ig ff c i fh eea iab ead d a i fi eg a i ib eh eed i e ia A e ed e f db e i eg a e a id ig d e i i ad i eadg i e i e h ich i eh e eab e c c h e i eg a eed fh ed a i fi eg a i ca i D iaec ag a b ih x [ a 1 , a 2 ] , y [ b 1 , b 2 ] , z [ c 1 , c 2 ] , h e h e j f a iab e h ee i a ea eed i id ea h eea e i i ea feg h x, y, , ad z each fh ee ig a b e ech ea i ( x * i , y * j , z * k ) ea a eh e f c i ca i f a ha i ad i h ee b h e e fh e b V = x y z eh e h ee f e e e fh eeb e ih i h ed a ih e i i fh ee a x, y, z a a ache i i eg a D f ( x, y, z ) dV eeF ig e fc eh eea e i ib e d e fi eg a iad f ec ag a d a i h eecaa b e i echaged fee : D f ( x, y, z ) dV = c 2 c 1 b 2 b 1 a 2 a 1 f ( x, y, z ) dxdydz = c 2 c 1 a 2 a 1 b 2 b 1 f ( x, y, z ) dydxdz = b 2 b 1 c 2 c 1 a 2 a 1 f ( x, y, z ) dxdzdy c F d a i h icha e ec ag a eca e ed h ec ce f e ead eeg i b eca d i ig ihb e ee ee e ! b e ig h e i ecea ;if eha eh ec ce eh db e ab e ied aa ia e i eg a E a e : eh ed a i fi eg a i cab ed ec ib eda D = { ( x, y, z ) | a x b, 1 ( x ) y 2 ( x ) , 1 ( x, y ) z 2 ( x, y ) } a h iF ig e h i ih eh eed i e ia eeg i h ii ea h iha a ic D i ageb ha eed ec ib ig ia id h e f adback id ea e a h ea e i h e a e x = a ad x = b ad h e e fad igh id e a ec ed i ed i e i ea...
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This note was uploaded on 04/05/2010 for the course MATH 119 taught by Professor Harmsworth during the Spring '08 term at Waterloo.

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Lectures32and33 - F ig e : i e eg a f ed ed h e eced igd ic...

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