# center of mass

• Apr 22nd 2009, 11:25 AM
mikegar813
center of mass
Find the center of mass (x,y) of the region bounded by the graphs of f(x)=4-x^2 and g(x)=x+2.
• Apr 22nd 2009, 12:06 PM
derfleurer
Another hint: take a triangular piece of paper. From each corner, draw a line to the middle of the opposite side. Each line will intersect at a particular point. That point is your center of mass.
• Apr 22nd 2009, 12:12 PM
running-gag
Hi

First draw the curves

http://nsa06.casimages.com/img/2009/...0310584161.jpg

Then compute the intersects of the 2 curves by solving $4-x^2 = x+2$
Spoiler:

$(x-1)(x+2)=0 \implies x=-2 \:or \:x=1$

The coordinates of the center of mass G are given by the formula

$x_G = \frac{\int\int x\:dx\:dy}{\int\int dx\:dy}$

$y_G = \frac{\int\int y\:dx\:dy}{\int\int dx\:dy}$

http://nsa06.casimages.com/img/2009/...0659270649.jpg
You can see that the area is defined by :
x between -2 and 1 ; y between (x+2) and 4-x² (see green line)

Therefore

Spoiler:

$x_G = \frac{\int_{-2}^{1}\int_{x+2}^{4-x^2} x\:dy\:dx}{\int_{-2}^{1}\int_{x+2}^{4-x^2} \:dy\:dx}$

$y_G = \frac{\int_{-2}^{1}\int_{x+2}^{4-x^2} y\:dy\:dx}{\int_{-2}^{1}\int_{x+2}^{4-x^2} \:dy\:dx}$
• Apr 22nd 2009, 12:39 PM
mikegar813
thanks but i dont understand double integers
• Apr 22nd 2009, 12:45 PM
running-gag
Quote:

Originally Posted by mikegar813
thanks but i dont understand double integers

You mean that you haven't studied double integrals ?
• Apr 23rd 2009, 03:51 AM
mikegar813
we have not learned double interals sorry