lecture17

lecture17 - MATH 100 Lecture 17 Triple Integral, I Class...

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2006 Fall MATH 100 Lecture 8 1 MATH 100 Lecture 17 Triple Integral, I bold the solid Assume density gaig with vavo solid a of mass the compute : Problem integrals Triple 17. Class
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2006 Fall MATH 100 Lecture 8 2 MATH 100 Lecture 17 Triple Integral, I k k V V G Δ by volume , by boxes (the label and solid the inside subboxes only the retain planes, coordinate the to parallel planes by subboxes smaller into divide : 1 Step = Δ n k k n n n n n n V z y x f z y x 1 * * * * * * ) , , ( sum Riemann partial the form and ), , , ( subbox each in point a pick : 2 Step
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2006 Fall MATH 100 Lecture 8 3 MATH 100 Lecture 17 Triple Integral, I ∫∫∫ ∫∫∫ ∫∫∫ ∫∫∫ ∫∫∫ ∫∫∫ ∫∫∫ ∫∫∫ ∫∫∫ ∫∫∫ + = = = = = Δ = = Δ = = = 2 1 ) , , ( ] , [ ) , , ( ) , , ( : integrals triple the of Properties 1 lim 1 ) , , ( when Remark, ) , , ( ) , , ( lim limit take and subboxes shrink the : 3 Step 2 1 1 1 * * * G G G G G G G G G n k k n G n k k n n n n fdV fdV dV z y x f G G G gdV fdV dV g f dV z y x f C dV z y x Cf dV V V(G) z y x f dV z y x f V z y x f m
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2006 Fall MATH 100 Lecture 8 4
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This note was uploaded on 09/17/2011 for the course MATH 100 taught by Professor Qt during the Fall '09 term at HKUST.

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lecture17 - MATH 100 Lecture 17 Triple Integral, I Class...

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