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Find the volumes of the solids described in Exercises 41–44. The solid bounded above by the hyperboloid with equationz=x2y2and bounded below by the square with vertices:(2,2,4),(2,2,4),(2,2,4),(2,2,4).

Short Answer

Expert verified

The volume of the described solid is: 0

Step by step solution

01

Step 1. Given Information  

The solid bounded above by the hyperboloid, z=x2y2

The solid bounded below by the square with vertices:

(2,2,4),(2,2,4),(2,2,4),and(2,2,4).

The region is:R={(x,y)|-2x2and-2y2}

02

Step 2. Finding the volume of given solid

The double integral to find the volume of the given solid is given by,

-22-22x2-y2dydx=-22x2y-y33-22dx=-22x2(2-(-2)-23-(-2)33dx=-224x2-163dx=4x33-16x3-22=4(23-(-2)3)3-16(2-(-2))3=643-643=0

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