Chapter 15, Problem 54RE

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Give five other iterated integrals that are equal to

To determine

**To express:** The given integral in five different ways.

Explanation

**Given:**

The iterated integral is,

**Calculation:**

Let *E* on *xy, yz* and *zx*-planes.

The variable *E* on *xy*-plane.

The graph of the above plane is shown below in Figure 1.

From Figure 1, it is observed that *x* varies from 0 to 8 and *y* varies from 0 to *z* varies from 0 to

Therefore,

The variable *E* on *yz*-plane.

The graph of the above plane is shown below in Figure 2.

From Figure 2, it is observed that *y* varies from 0 to 2 and *z* varies from 0 to *x* varies from 0 to

Therefore,

The variable *E* on *xz*-plane.

The graph of the above plane is shown below in Figure 3.

From Figure 3, it is observed that *x* varies from 0 to 4 and *z* varies from 0 to *y* varies from 0 to

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