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Chapter 13: Q. 63 (page 1005)

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)=xy+yxWhereR={(x,y)|1鈮�x鈮�3,1鈮�y鈮�5}

Short Answer

Expert verified

The volume is4ln(4)+12ln(3)cubicunits

Step by step solution

01

Given information

We are given a rectangular region

f(x,y)=xy+yxWhereR={(x,y)|1鈮�x鈮�3,1鈮�y鈮�5}

02

Evaluate the integral

We have,

鈭�Rxy+yxdA=鈭�15鈭�13xy+yxdxdy=鈭�15[x22y+ylnx]31dy=鈭�15(4y+ln(3))ydy=[4lny+ln(3)y22]51=4ln(4)+12ln(3)

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Most popular questions from this chapter

Evaluate each of the integrals in exercise 33-36 as iterated integrals and then compare your answers with those you found in exercise 29-32

鈭�鈭�Rx2y3dAWhereR={(x,y)|1鈮�x鈮�3,0鈮�y鈮�2}

Evaluate the iterated integral :

鈭�0蟺/2鈥�鈭�0cos鈦�y鈥�鈭�0sin鈦�y鈥�(2x+y)dzdxdy

How many summands are in 鈭�i=i0l鈭�j=j0m鈭�k=k0nkijk?

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 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�Rx2ydAWhereR={(x,y)|-1鈮�x鈮�0,0鈮�y鈮�2}
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