Chapter 15.6, Problem 50E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

If *E* is the solid of Exercise 18 with density function

(a) The mass

(b) The center of mass

(c) The moment of inertia about the *z*-axis

To determine

**To find:**

The exact value of the mass for

Explanation

**1) Concept:**

If the density function of a solid object that occupies the region

**2) Given:**

The density function

**3) Calculation:**

We have,

Consider

Thus,

But region is first octant, therefore consider positive

Therefore, we get,

Thus, using

Evaluating this integration using the Computer Algebra System,

Write following command on Mathematica,

This gives the output as,

This can also be rewritten as

**Conclusion:**

**To find:**

The exact value of the center of mass for

**Solution:**

The center of mass is

**1) Concept:**

The center of mass located at the point

And its moments about three coordinate planes are,

**2) Given:**

The density function

**3) Calculation:**

We have,

Thus,

Therefore, we get

Thus, using

Therefore,

Evaluating this integration using the Computer Algebra System,

Since

Write following command on Mathematica

This gives the output as,

This approximates to

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