In the first problem you are given and are asked to find it flux out of the ball . (you have but that is corrected in the integral so I assume that was a typo).

You do the integral by writing it as and then try to calculate , , and . You realize, do you not that those are just the coordinates of thecenterof the figure? Here that figure is a sphere with center at (2, 0, 3) so you should be able to write down, with no calculation at all, that , , and .

I have no idea at all how you got " "! You understand, don't you, that the x coordinate of the centroid of a figure is anumbernot a function of x? And it certainly is NOT the case that !