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Chapter 13: Q. 38 (page 1055)

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

鈭02鈭03鈭4x/34f(x,y,z)dzdxdy

Short Answer

Expert verified

The three-dimensional region is,

鈩=(x,y,z)/0鈮x鈮3,0鈮y鈮2,4x3鈮z鈮4

Step by step solution

01

Step 1. Given Information 

We are given,

鈭02鈭03鈭4x/34f(x,y,z)dzdxdy

02

Step 2. The three dimensional region. 

By the definition of triple integral 鈭a1a1鈭b1b2鈭c1c2f(x,y,z)dzdydxrepresent the volume of the solid region 鈩=(x,y,z)鈭a1鈮x鈮a2,b1鈮y鈮b2,c1鈮z鈮c2

Using this definition, we get

Given triple integral 鈭02鈭03鈭4x34f(x,y,z)dzdxdyrepresents the volume of rectangular solid represents by 鈩=(x,y,z)/0鈮x鈮3,0鈮y鈮2,4x3鈮z鈮4.

Since by the triple integral the limits are0鈮x鈮3,0鈮y鈮2,4x3鈮z鈮4.

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Most popular questions from this chapter

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

f(x,y)=-2x2y3WhereR={(x,y)|-2鈮x鈮3,-1鈮y鈮5}

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Evaluate the iterated integral :

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