1.Find the area, mass, and center of mass of a thin plate bounded by and with density .

Computing these, should be OK. Just wondering about the limits of integration. Would it be to and to ?

2.Let

Show that , but that does not exist.

Then this implies that or . So we only integrate it when ? And for the second case, the function may be similar to which does not exist?

The only problem is, when we are integrating from to , we integrate over both rationals and irrationals. So maybe the second case deals with this, and that is why it doesn't exist. Whereas, in the first case, we keep constant, and integrate over the rationals between and ?