Chapter 15.6, Problem 33E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

The figure shows the region of integration for the integral

Rewrite this integral as an equivalent iterated integral in the five other orders.

To determine

**To express:** The integral

Explanation

**Given:**

The region of the given integral is given in the form of figure.

The region are

**Calculation:**

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

Since the variable *E* on *xy*-plane, set

Then, the equation becomes,

The graph of the *xy*-plane is shown below in Figure 1.

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

Therefore,

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

The graph of the *yz*-plane is shown below in Figure 2.

From Figure 2, it is observed that *z* varies from 0 to 1, *y* varies from 0 to *x* varies from 0 to

Therefore,

Also, from Figure 2, it is observed that *y* varies from 0 to 1, *z* varies from 0 to *x* varies from 0 to

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

The graph of *yz*-plane is shown below in Figure 3.

From Figure 3, it is observed that *x* varies from 0 to 1, *z* varies from 0 to *y* varies from

Therefore,

Also, from Figure 3, it is observed that *z* varies from 0 to 1, *x* varies from 0 to *y* varies from

Therefore,

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