Center of mass of solid hemisphere by using angle as variable.

[AlchemistK]

Homework Statement

I've just started with center of mass, and instead of the method in the book, I tried solving the center of mass for a solid hemisphere using angle as a variable, but the answer didn't match.
A small disk of mass "dm" is taken, which subtends an angle "dθ" at the center.The total mass of the hemisphere is "M". Please refer to the attachment for the figure and my full attempt.
Where have i gone wrong?

Homework Equations

y(cm) = ∫y dm / ∫ dm = 1/M (∫y dm)

The Attempt at a Solution

Please refer to the attachment.

 

[micromass]

Mod Note: moved to calculus & beyond. Please post in the correct forum next time!

 

[AlchemistK]

Ah. Never mind, I found my mistake. Very idiotic of me.