1. The problem statement, all variables and given/known data Let R be the region in the first quadrant (x,y ≥ 0) bounded by the lines [itex]y = x - 1[/itex] and [itex]y = x + 1[/itex] and the circles [itex]x^2 + y^2 = 1[/itex] and [itex]x^2 + y^2 = 10[/itex] Evaluate the integral : [itex]\int \int_R (x^2 + y^2)^2(y-x)^2(y+x)dxdy[/itex] 2. Relevant equations Polar co-ordinates, maybe substitution? 3. The attempt at a solution So at first I considered x = rcosθ and y = rsinθ. So our lines turn into : r(cosθ - sinθ) = 1 and r(sinθ - cosθ) = 1 Our circles become : r = 1 and r = √10 ( Some nice bounds for r ). My problem now is how to find my limits for theta. I'm having trouble seeing it since the lines don't exactly turn into something nice.