1. The problem statement, all variables and given/known data The problem and its solution are attached as TheProblemAndTheSolution.jpg. If you don't want to view the attached image, the cartesian-coordinate version that the problem wants me to convert to a polar-coordinate version is the following (let "int" = "integral").: int int (1 - x^2 - y^2) dx from 0 to sqrt(2y - y^2) dy from 0 to 1 2. Relevant equations Let t = theta (because it is simpler to type). Then x = rcos(t), y = rcos(t), r^2 = x^2 + y^2 3. The attempt at a solution I completed the square and got this circle ( http://www.wolframalpha.com/input/?i=plot x^2 + (y - 1)^2 = 1 ). Let "int" = "integral". I thought I was supposed to do int int (1 - r^2) r dr from 0 to 1 (because the radius ranges in size from 0 to 1) dt from 0 to pi (because, I was initially thinking 0 to -pi, but then I thought about the circle being above the x axis and that the area would be positive). Why does the solution attached get what it gets?