How do I calculate center of mass using integrals and density?

[aaronfue]

Just some things I need to verify:

When finding the x-bar of the function y=x³ using the equation:

\bar{x} = \frac{∫\tilde{x}dm}{∫dm},

Is my \tilde{x} going to be the x distance(which will just be "x") times x³?

Also, will x³ be in the denominator just before "dm"?

The same process is done for the \tilde{y}, am I correct?

If I am also given a density \rho, will that stay in front of each integrand or in front of (\frac{∫\tilde{x}dm}{∫dm})?

Is the same process is done for the \tilde{y} or are there differences?

Thanks!

 

[Simon Bridge]

https://www.physicsforums.com/showthread.php?t=650874