Chapter 15.4, Problem 19E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Find the moments of inertia *I _{x}, I_{y}*,

To determine

**To find:** The moments of inertia

Explanation

**Formula used:**

The moments of inertia is,

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

**Given:**

The region *D* is the isosceles triangle with equal sides of length *a.*

The density function is proportional to the square of the distance from the vertex opposite to the hypotenuse, that is

**Calculation:**

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

Integrate with respect to *y* and apply it’s limit.

Integrate with respect to *x* and apply it’s limit.

Simplify it further,

The moments of inertia

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