Chapter 15.4, Problem 3E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Find the mass and center of mass of the lamina that occupies the region *D* and has the given density function *ρ.*

**3.** *D =* {(*x*, *y*) | 1 ≤ *x* ≤ 3, 1 ≤ *y* ≤ 4}; *ρ*(*x, y*) = *ky*^{2}

To determine

**To find:** The total mass and the center of mass of the lamina.

Explanation

**Given:**

The region *D* is

The density function is

**Formula used:**

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 center of mass of the lamina that occupies the given region *D* is

Here,

If

**Calculation:**

The total mass of the lamina is,

Integrate with respect to *x* and *y* by using (1),

Apply the limit value of *x* and *y*,

=

In order to get the coordinates of the center of mass, find

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