It's a semi-circle. Your theta limits should be 0 to , surely. Perhaps it would be easier to change it to a polar double integral straight from the beginning.

And the integrand in the formula for a centroid is y, not 1.

Hence:

You should find that this equates to

For the x coordinate it's the same story only we use , and your integral should turn out to be zero.

As a general rule of thumb, if a body is symmetrical around a particular axis, then the coordinate of the centroid in the perpendicular axis will be in the centre of the body. i.e., your semicircle is centered at the origin, and is symmetric around the y axis. Hence you can jump straight to the conclusion that the x coordinate of the centroid will be in the centre of the body with respect to the x axis... hence at zero.