help

[lilkrazyrae]

Hey so here is the problem. Find the center of mass of a thin plate of constant density covering the given region.
The region bounded by y=x^4, x=3, and the x-axis.
I tried to use the equation for the moment about the origin and the mass to find the center of mass but i came up with the wrong answer! How do you know what equations to use and in what order, which ones are used in this problem?
thanks

 

[galactus]

I hope someone corrects me if I'm wrong. It's been awhile since I done these. I believe you need double integrals. I wish I knew how to type them on this site.

The area of the centroid is given by the double integral.

Area=double integral(dydx, y=0..x^4, x=0..3)=243/5

double integral(ydydx, y=0..x^4, x=0..3)=2187/2

double integral(xdydx, y=0..x^4, x=0..3)=243/2

(5/243)(2187/2)=45/2

(5/243)(243/2)=5/2

Centroid=(5/2, 45/2)

I hope I could help some.

 

[lilkrazyrae]

thanks

hey thanks that all works out except the 45/2 is the y value and the 5/2 is the x value!!!

 

[lilkrazyrae]

question

just one question I understand how you got the first two integrals but on the third one how did you get it?

 

[galactus]

I had my figures backwards. Sorry. You were right. The centroid of a region, say, R is given by double integrals.

The first one is the area; the 2nd one is y-bar, I believe this is called the first moment of the lamina about the x-axis; the third one is x-bar, the first moment of the lamina about the y-axis. When you evaluate centroids, like this one, you need a double integral for the area, one for x, and one for y. A centroid is what you have when the density function is constant.

I hope this helps