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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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 .
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

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.

Page1 / 5

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online