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Chapter 13: Q.25 (page 1082)

Evaluating triple integrals: Each of the triple integrals that follow represents the volume of a solid. Sketch the solid and evaluate the integral.

鈭02鈭14鈭-23dxdydz

Short Answer

Expert verified

The value of the triple integral is 30.

Step by step solution

01

Step 1. Given information.

Consider the given information.

鈭02鈭14鈭-23dxdydz

02

Step 2. Graph the solid.

By using the limits, sketch the given solid.

-2鈮x鈮31鈮y鈮40鈮z鈮2

And,

03

Step 3. Calculate the integral.

Integrate by using limit and solve.

鈭02鈭14鈭-23dxdydz=鈭02鈭14x-23dydz=鈭02鈭143--2dydz=5鈭02y14dz=5鈭024-1dz=15z02=30

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Most popular questions from this chapter

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 Each of the integrals in exercises 33-36 as an iterated integral and then compare your answer with thoise you found in exercise 29-32

鈭鈭RxydAWhereR={(x,y)|0鈮x鈮2,1鈮y鈮4}

Evaluate the triple integrals over the specified rectangular solid region.

鈭R鈥zsin鈦xcos鈦ydV,whereR=(x,y,z)鈭0鈮x鈮蟺,3蟺2鈮y鈮2蟺,and1鈮z鈮3

Evaluate each of the double integrals in Exercises 37鈥54 as iterated integrals.

鈭鈭RxexydA,where{R=(x,y)|0鈮x鈮1and0鈮y鈮ln5}

Find the volume between the graph of the given function and the xy-plane over the specified rectangle in the xy-plane

f(x,y)=sinxcosyWhereR={(x,y)|0鈮x鈮蟺,0鈮y鈮蟺}
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