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.

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- Apr 22nd 2009, 11:25 AMmikegar813center 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 PMderfleurer
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 PMrunning-gag
Hi

First draw the curves

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

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

__Spoiler__:

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

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

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

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__: - Apr 22nd 2009, 12:39 PMmikegar813
thanks but i dont understand double integers

- Apr 22nd 2009, 12:45 PMrunning-gag
- Apr 23rd 2009, 03:51 AMmikegar813
we have not learned double interals sorry