I have to calculate the centre of mass of the drawn hemisphere. I don't understand where I make mistakes. The process I followed on the above image is the following: (I) Here I simply translated position vector components from cartesian to polar coordinates. (II) Formula of x-component of position vector of centre of gravity (this position vector clearly lies on the x-axis, so I'm interested only in this component) (III) This is the volume element for polar coordinates system. After that, I just put (III) into (II). The problem is that, the result of the last (triple) integral (computable easily with wolfram alpha) seems to result zero! I thought that the mistake could be in the integration limits, but they look to be correct. Where am I doing wrong? Thank you very much in advance.