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Chapter 13: Q. 58 (page 1005)

Find the signed volume between the graph of the function and the xy-plane over the specified region

f(x,y)=xy3ex2y2WhereR={(x,y)|-2鈮�x鈮�-1,-2鈮�y鈮�0}

Short Answer

Expert verified

The value of the volume is-6-2e4+8e16cubicunits

Step by step solution

01

Given information

We are given a function over a region

f(x,y)=xy3ex2y2WhereR={(x,y)|-2鈮�x鈮�-1,-2鈮�y鈮�0}

02

Find the volume

The value of the function is positive in the given region

Hence the volume becomes

鈭�-20鈭�-2-1xy3ex2y2dxdyV=2鈭�-20[yex2y2]-1-2dyV=2鈭�-20[yey2-ye4y2]dyV=[2ey2-8e4y2]-20V=[-6-2e4+8e16]

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