This double integral is actually the volume under a 3-D “bell”
Rectangles aren’t the only thing that integrates! We can now do a clever change of variable by converting to Polar coordinates!
How polar coordinates work, and how to make the switch... Any integral can be computed by the limit of Riemann sums over Cartesian rectangles or Riemann sums over polar rectangles. The area of a Cartesian rectangle of sides dx and dy is dx*dy but the area of a polar rectangle of sides dr and dt is NOT just dr*dt
Rather dA is a bit more... Getting back to our story...
Recall the Pythagorean Theorem? We can now do a clever change of variable by converting to Polar coordinates!