Chapter 15.4, Problem 22E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

A lamina with constant density *ρ* (x, y) *= ρ* occupies the given region. Find the moments of inertia *l _{x}* and

**22**. The triangle with vertices (0, 0), (*b*, 0), and (0, *h*)

To determine

**To find:** The moments of inertia about *x* and *y* axes

Explanation

**Given:**

The density function,

The region *D* is the triangle with vertices

**Formula used:**

The moments of inertia is,

The total mass of the lamina is,

Here, the density function is given by
*D* is the region that is occupied by the lamina.

The radii of gyration about *y* and *x* axis is respectively

**Calculation:**

Obtain the equation of the line joining the points

From the given conditions, it is observed that, *x* varies from 0 to *b* and *y* varies from 0 to

Obtain the moments of inertia

Integrate with respect to *y.*

Integrate with respect to *x.*

=

Obtain the moments of inertia

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