Imagine a thin washer with centre at the centre of the disc, internal radius and external radius (so its width is ). Its internal circumference is , and its area is therefore approximately .
The density at a distance from the centre is units of mass per unit of area. So the mass of this washer is
To get the mass of the whole disc you'll need to work out the integral of this expression (with replaced by ), with limits to .
Can you do it now?