Calculate Star Mass from Radius: An Integration Approach

[Unto]

Sorry no one was answering my question, and I just wanted to get this done:

Homework Statement

...Hence show that the mass of the star is M = [tex]4\pi[/tex][tex]p_{c}[/tex][tex]\left(R^{3}/3 )[/tex]

Homework Equations

M(r) = [tex]4 \pi[/tex][tex]p_{c}[/tex][tex]\left(r^{3}/3 - r^{4}/4R)[/tex]
This is the mass within a radius

The Attempt at a Solution

I already found the mass within a radius via intergration (look at relevant equations), and I know that I have to build up an 'infinite' number of radial masses to get the whole mass of the star. But do I use integration on this equation or something else? What do I do?

 

[Unto]

Oohh for f_cks sake... I realized

Total radius of the star is 'R'. Just substitute that in for [tex]r[/tex] and cancel, since r1 is subjective and doesn't factor for the whole star.

WHHHYYYYYY!??

 

[Matterwave]

The total mass of anything is just M=pV where p is the average density and V is the volume. Here V=4/3*pi*R^3. That's that...