1. The problem statement, all variables and given/known data Evaluate by changining to polar coordinates : #19 in this picture http://i52.tinypic.com/2ngbt5z.jpg 2. Relevant equations x = cos θ y = sin θ r^2 = x^2 + y^2 + z^2 ∫∫∫w f(x,y) dxdy = ∫from θ1 to θ2 ∫from r1 to r2 f(cosθ, sinθ) (r dr dθ) 3. The attempt at a solution The first thing I did is sketch y = (2x-x^2)^(1/2) in xy plane. y = (2x-x^2)^(1/2) y^2 = 2x-x^2 0 = y^2 - 2x + x^2 0 = y^2 + (x^2-2x+1) -1 1 = y^2 + (x-1)^2 ====> circle with radius one, centered around (1,0). I also graphed y=0, x=1, and x=2. We know that we want the region between x=1 and x=2, and it is in postive y-axis due to y = 0. so we have a quarter of a circle that we need integral. I am stuck here, I do not what the bounds for θ and r are. I think the bounds for θ is 0 ≤ θ ≤ pi/4 but not too sure. I have no clue how to find the r for the problem.... I know it cannot be 1 ≤ r ≤ 2. I know how to change the given function into polar but I need help finding the bounds, if someone can help me out, please, thanks in advance.