Lecture15 - Lecture 15 Triple Integrals June 4 2009 Lecture 15 Triple Integrals Objectives 1 Compute triple integrals over rectangular boxes 2

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Unformatted text preview: Lecture 15: Triple Integrals June 4, 2009 Lecture 15: Triple Integrals Objectives 1 Compute triple integrals over rectangular boxes. 2 Compute triple integrals over more general regions. 3 Use triple integrals to compute volumes. 4 Use triple integrals to compute centers of mass. Lecture 15: Triple Integrals Triple integrals over boxes Suppose R = [ a , b ] × [ c , d ] × [ r , s ] is a rectangular region and f = f ( x , y , z ). ZZZ R f ( x , y , z ) dxdydz = Z s r Z d c Z b a f ( x , y , z ) dxdydz Lecture 15: Triple Integrals Triple integrals over boxes Suppose R = [ a , b ] × [ c , d ] × [ r , s ] is a rectangular region and f = f ( x , y , z ). ZZZ R f ( x , y , z ) dxdydz = Z s r Z d c Z b a f ( x , y , z ) dxdydz Fubini’s Theorem: We can integrate in any order. Lecture 15: Triple Integrals Triple integrals over general regions 1 Type I R = { ( x , y , z ) | ( x , y ) ∈ Du 1 ( x , y ) ≤ z ≤ u 2 ( x , y ) } 2 Type II R = { ( x , y , z ) | ( y , z ) ∈ Du 1 ( y , z ) ≤...
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This note was uploaded on 04/29/2010 for the course MATH 200 taught by Professor Unknown during the Spring '03 term at The University of British Columbia.

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Lecture15 - Lecture 15 Triple Integrals June 4 2009 Lecture 15 Triple Integrals Objectives 1 Compute triple integrals over rectangular boxes 2

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