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12.7- Triple Integrals 1. The formulas for the mass and center of mass for a 3D object are natural extensions of the formulas for a 2D object: m = Myz = | x P(x, y, z) av JM.y p(x. y. 2) dv Mxy = ||| z p(x, y, z) dV Mxz = Myz = Mxz ỹ : m Mgy m m Suppose an object occupies the rectangular cube D = { (x, y, z)| – 1sx< 1,0 < y< 4,–3

12.7- Triple Integrals 1. The formulas for the mass and center of mass for a 3D object are natural extensions of the formulas for a 2D object: m = Myz = | x P(x, y, z) av JM.y p(x. y. 2) dv Mxy = ||| z p(x, y, z) dV Mxz = Myz = Mxz ỹ : m Mgy m m Suppose an object occupies the rectangular cube D = { (x, y, z)| – 1sx< 1,0 < y< 4,–3

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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12.7- Triple Integrals 1. The formulas for the mass and center of mass for a 3D object are natural extensions of the formulas for a 2D object: m = Myz = | x P(x, y, z) av JM.y p(x. y. 2) dv Mxy = ||| z p(x, y, z) dV Mxz = Myz = Mxz ỹ : m Mgy m m Suppose an object occupies the rectangular cube D = { (x, y, z) | – 1<x< 1,0 < y< 4, -3 <z<0}, with a density function of p(x, y, z) = y. Find the total mass and center of mass.
Transcribed Image Text:12.7- Triple Integrals 1. The formulas for the mass and center of mass for a 3D object are natural extensions of the formulas for a 2D object: m = Myz = | x P(x, y, z) av JM.y p(x. y. 2) dv Mxy = ||| z p(x, y, z) dV Mxz = Myz = Mxz ỹ : m Mgy m m Suppose an object occupies the rectangular cube D = { (x, y, z) | – 1<x< 1,0 < y< 4, -3 <z<0}, with a density function of p(x, y, z) = y. Find the total mass and center of mass.
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