I'm in the middle of the Great Courses Multivariable Calculus course. A double integral example involves a quarter circle, in the first quadrant, of radius 2. In Cartesian coordinates, the integrand is y dx dy and the outer integral goes from 0 to 2 and the inner from 0 to sqrt(4-y^2). In polar, the integrand is (r sin theta) r dr dtheta, with the outer going from 0 to pi/2 and inner from 0 to 2. The final result, in both forms, is 8/3. My thinking was that this would describe the area of the quarter circle, but elementary geometry tells me the area should be pi. I'm trying to visualize what this value of 8/3 represents. Maybe this sounds stupid, but I could use some help.