Write a double integral that can be evaluated to tell you how much dirt you need

to fill the hole.

$[$Hint: you can assume that this is the only hole in the entire $($flat$)$ universe, such that the

definition of $f(x,y)$ above is valid for all xin$(-,),$yin$(-,).]$

Evaluate the integral in the previous question in a coordinate system that is not

the standard cartesian system.

$[$Hint: look at the form of the integrand to figure out a coordinate transformation to

make the integral easier to solve.$]$