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Homework Statement
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
Homework Equations
Let t = theta (because it is simpler to type). Then x = rcos(t), y = rcos(t), r^2 = x^2 + y^2
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?
Attachments
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