I have no idea how to solve the double integral for the function. Could I get some help please?
Here's a non-rigorous (but essentially correct) way to tackle this. For 0 ≤ t ≤ 1, the set is L-shaped, consisting of two line segments each of length t. Thus it has "infinitesimal area" 2tdt, and therefore . You can integrate this by parts, but the answer will have to involve the error function. Numerically, I make it approx. 1.9715.