Chapter 15.6, Problem 35E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Write five other iterated integrals that are equal to the given iterated integral.

**35**.

To determine

**To express:** The integral

Explanation

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 1 and *y* varies from 0 to *x* and *z* varies from 0 to *y*.

Hence,

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 1 and *z* varies from 0 to *x* varies from *y* to 1.

Hence,

Therefore,

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

Hence,

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 1 and *z* varies from 0 to *x* and *y* varies from *z* to *x*.

Hence,

Therefore,

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

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