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Chapter 13: Q 5. (page 1038)

Identify the quantities determined by the integral expressions

蚁(x,y)is a density function in grams per square centimeter

鈭�惟xdA鈭�惟dAand鈭�惟ydA鈭�惟dA

Short Answer

Expert verified

The quantities determines center of mass.

Step by step solution

01

Given Information

The given expressions are

鈭�惟xdA鈭�惟dAand鈭�惟ydA鈭�惟dA

x,yis in centimeter.

02

Identification of the quantities

鈭�惟xdA鈭�惟dArepresents center of mass within region 惟having constant density function 蚁(x,y)=1measured from yaxis in centimeters.

x炉=鈭�惟xdA鈭�惟dA

Similarly

鈭�惟ydA鈭�惟dArepresents center of mass within region having constant density function 蚁(x,y)=1measured from xaxis.

y炉=鈭�惟ydA鈭�惟dA

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Most popular questions from this chapter

Howmanysummandsarein鈭�j=j0m鈭�k=k0njk?

Let 惟be a lamina in the xy-plane. Suppose 惟is composed of n non-overlapping lamin忙 role="math" localid="1650321722341" 惟1,惟2,鈥�,惟n.Show that if the masses of these lamin忙 are m1,m2,鈥�,mnand the centers of masses are x炉1,y炉1,x炉2,y炉2,鈥�,x炉n,y炉n,then the center of mass of 惟is x炉,y炉,where

x炉=鈭�k=1nmkx炉k鈭�k=1nmkandy炉=鈭�k=1nmky炉k鈭�k=1nmk.

Evaluate the sums in Exercises 23鈥�28.

鈭�j=13鈭�k=12jk

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

鈭�03鈭�03鈭�03-yf(x,y,z)dzdydx

Evaluate the triple integrals over the specified rectangular solid region.

鈭�R鈥�x2yzdV, whereR={(x,y,z)鈭�鈭�2鈮�x鈮�1,0鈮�y鈮�3,and1鈮�z鈮�5}
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