Moment Of Inertia (calc vs physics different answer)

I'm trying to understand Moment Of Inertia using integration.

But it seems the calculus definition of physics definition are different.
(I'm trying to apply my math skill to physics)

example of apparent contradiction:

here:http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html#mi
it says the moment of inertia of "hoop about symmetric axis" is

m*r^2

but here:
page 21 of the book:
http://www.eng.auburn.edu/~marghitu/MECH2110/C_4.pdf
says the moment of inertia of a circle centered at (0,0) about the z-axis is

Pi r^4 /4

does this mean the mass of a circle is "Pi r^2/4"

my goal: be able to calculate the moment of inertia of a, x-y planar figure about the z-axis, given the parametric (or polar) equation of the curve.

please help me solve the apparent contradiction between the calculus and physics definition of moment of inertia