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Describe the three-dimensional region expressed in each iterated integral in Exercises 35–44.

-33-9-y29-y209-y2-z2f(x,y,z)dxdzdy

Short Answer

Expert verified

The three-dimensional region represents the volume of the region is the right by the parabolic x=9-y2-z2bounded on the left by the yz plane. ,

Step by step solution

01

Step 1. Given Information.

We are given,

-33-9-y29-y209-y2-z2f(x,y,z)dxdzdy

02

Step 2. The three dimensional region. 

By the definition of triple integral a1a1b1b2c1c2f(x,y,z)dzdydxrepresent the volume of the solid region =(x,y,z)a1xa2,b1yb2,c1zc2

Using this definition, we get

The given triple integral represents the volume of the region is the right by the parabolic x=9-y2-z2 bounded on the left by the yz plane.

Since from the given integral we observe that

x=9-y2-z2

Which represent the parabolic region and

z=9-y2

It represent yz plane.

Thus, the given iterated integral represents the volume of the region is the right by the parabolic x=9-y2-z2bounded on the left by the yz plane.

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