# 11.02 - Section 12.5: Triple integrals Main ideas? .?....

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Section 12.5: Triple integrals Main ideas? ..?. . Triple Riemann sums. The basic definition of a triple integral. The triple Fubini theorem. The triple integral on a general domain. The various types of volume domain, and how to set up the volume integral based on each of them. Changing the order of integration in triple integrals. Recall that A × B × C = {( x , y , z ): x in A , y in B , z in C }. If B is a rectangular box [ a , b ] × [ c , d ] × [ r , s ] = {( x , y , z ) in R 3 : a x b , c y d , r z s } and f ( x , y , z ) has domain B , then a triple Riemann sum for f is (*) Σ i =1 l Σ j =1 m Σ k =1 n f ( x ijk *, y ijk *, z ijk *) V ijk where: a = x 0 < x 1 < … < x l = b , c = y 0 < y 1 < … < y m = d , and r = z 0 < z 1 < … < z n = s ; V ijk is the volume of the box B ijk = [ x i –1 , x i ] × [ y i –1 , y i ] × [ z i –1 , z i ]; and ( x ijk *, y ijk *, z ijk *) is in B ijk .

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## This note was uploaded on 02/13/2012 for the course MATH 241 taught by Professor Staff during the Fall '11 term at UMass Lowell.

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11.02 - Section 12.5: Triple integrals Main ideas? .?....

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