28.

2130. Cartesian to polar coordinates Evaluate the following integrals using polar coordinates. Assume (r, 6) are polar coordinates. A sketch is helpful. 28. 3 So 9-x2 Vx2 + y? dy dx\f34. The solid bounded by the paraboloids z = 2x2 + y and Z = 27 - x2 - 2y2 Z = 27 - x2 - 2y2 z = 2x2 + 12 R X6568. Improper integrals Improper integrals arise in polar coordinates when the radial coordinate r becomes arbitrarily large. Under certain conditions, these integrals are treated in the usual way: f f - ' '9 b a a 8039) I\" d!\" d9 bllm fa fa 3036) rdr d6. Use this technique to evaluate the following integrals. 68. dA R (1+x2412)2, K is the first quadrant