/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 2 Let 伪,尾,纬,未,系,and聽味聽be r... [FREE SOLUTION] | 91影视

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Chapter 13: Q. 2 (page 1041)

Let 伪,尾,纬,未,系,and味be real numbers, and let 蚁(x,y,z)be a function giving the density at each point of a three-dimensional rectangular solid. What does the triple integral鈭�伪尾鈭�纬未鈭�系味蚁(x,y,z)dzdydxrepresent?

Short Answer

Expert verified

The triple-iterated integral represents volume.

鈭�伪尾鈭�纬未鈭�系味蚁(x,y,z)dzdydx=鈭�鈩�蚁(x,y,z)dV

Step by step solution

01

Step 1. Given information. 

The given integral is鈭�伪尾鈭�纬未鈭�系味蚁(x,y,z)dzdydx.

02

Step 2. Explanation. 

If 伪,尾,纬,未,系,and味are real numbers, and 蚁(x,y,z)isa function giving the density at each point of a three-dimensional rectangular solid, then

鈭�伪尾鈭�纬未鈭�系味蚁(x,y,z)dzdydx=鈭�伪尾鈭�纬未鈭�系味蚁(x,y,z)dzdydx鈭�伪尾鈭�纬未鈭�系味蚁(x,y,z)dzdydx=鈭�鈩�蚁(x,y,z)dV

So the integral represents the volume.

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Most popular questions from this chapter

Use the lamina from Exercise 64, but assume that the density is proportional to the distance from the x-axis.

In the following lamina, all angles are right angles and the density is constant:

Describe the three-dimensional region expressed in each iterated integral in Exercises 35鈥�44.

鈭�-33鈭�-9-z29-z2鈭�03-x2+z2f(x,y,z)dydxdz

In Exercises 57鈥�60, let R be the rectangular solid defined by

R = {(x, y, z) | 0 鈮� x 鈮� 4, 0 鈮� y 鈮� 3, 0 鈮� z 鈮� 2}.

Assuming that the density at each point in R is proportional to the distance of the point from the xy-plane, find the moment of inertia about the x-axis and the radius of gyration about the x-axis.

LetR=x,y,z|a1猢�x猢�a2,b1猢�y猢�b2,c1猢�z猢�c2.Provethat:鈭�RdV=a2-a1b2-b1c2-c1.WhatistherelationshipbetweenRandtheproducta2-a1b2-b1c2-c1.
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