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

-33-9-x29-x2-33f(x,y,z)dzdydx

Short Answer

Expert verified

The three-dimensional region is given by the equation,

x2+y2=32

It represent the represents the volume of the cylinder of radius 3and height 3.

Step by step solution

01

Step 1. Given Information.

We are given,

-33-9-x29-x2-33f(x,y,z)dzdydx

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

Given triple integral -339-x29-x2-33f(x,y,z)dzdydxrepresents the volume of the cylinder of radius 3and height 3.

Since from the given iterated integral we observe that

role="math" localid="1650352416990" y=9-x2x2+y2=9x2+y2=32

Which represent the circle of radius 3 and center at origin.

The top of the cylinder is a circle.

Hence it represent the represents the volume of the cylinder of radius 3and height 3.

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