Need help finding center of mass

[_MNice_]

A solid is formed by rotating the region bounded by the curve y=e^(-6x/2) and the x-axis between x=0 and x=1 , around the -axis. The volume of this solid is (pi/6)(1-e^(-6)). Assuming the solid has constant density, find the center masses of x and y.


center of mass (x or y)= (integral(x*density*f(x)dx)/mass


I know I need to do something with the mass and the x=o,1, but I don't know how to do it. I know that density*volume=mass, so i think i have to do something with that. Maybe find the mass at x=0 and x=1 and then find the center of that, but I'm really not sure.

Thanks!

 

[HallsofIvy]

Are you not taking a Calculus course? Does your textbook not have a discurssion and formula for center of mass? You seem to be saying that you do not know anything at all about this. For one thing, single points do not have a "mass" only extended bodies do.

Strictly speaking, because this is purely a geometric problem and there is no "mass" or "density" function given, you are talking about the "centroid", not "center of mass".

The centroid of a solid figure, R, is $(x_0, y_0, z_0)$ where
$$x_0= \frac{\int_R xdV}{\int_R dV}= \frac{\int_R xdV}{Volume}$$
$$y_0= \frac{\int_R ydV}{\int_R dV}= \frac{\int_R ydV}{Volume}$$
$$z_0= \frac{\int_R zdV}{\int_R dV}= \frac{\int_R zdV}{Volume}$$