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Chapter 13: Q. 59 (page 1005)

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

f(x,y)=xyWhereR={(x,y)|-2鈮�x鈮�3,-1鈮�y鈮�5}

Short Answer

Expert verified

The value of integral is 24cubicunits

Step by step solution

01

Given information

We are given an region

f(x,y)=xyWhereR={(x,y)|-2鈮�x鈮�3,-1鈮�y鈮�5}

02

Find the volume

f(x,y)>0whenR1={(x,y)|0鈮�x鈮�3,0鈮�y鈮�5}andf(x,y)<0whenR1={(x,y)|-2鈮�x鈮�0,-1鈮�y鈮�0}

And

鈭�RxydA=鈭�R1xydA-鈭�R2xydA=鈭�05鈭�02xydxdy-鈭�-10鈭�-20xydxdy=[x2y24]-[x2y24]=25-1=24cubicunits

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Most popular questions from this chapter

Use the results of Exercises 59 and 60 to find the centers of masses of the lamin忙 in Exercises 61鈥�67.

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