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