nprofile1qy2hwumn8ghj7un9d3shjtnddaehgu3wwp6kyqpqqxljff9c9erzmwzufdp877ade74trj5cxlag8x05vn7xx6x6nsfq7tyg3m (nprofile…yg3m) I did it as an integral from first principles, and also using Mathematica’s boolean operations on its Region structures, and I got the same answer by both methods.
You can probably cajole Wolfram Alpha into doing boolean operations on regions as well, but I haven’t tried; I guess it takes verbatim Mathematica code, though sometimes it gets sulky because it wants you to flatter it by pretending it can interpret natural language.