APPM 2350 Final: appm2350summer2014examfinal_sol
Document Summary
Summer 2014: (50 points) suppose you nd yourself in a parallel universe where the local force due to gravity takes the improbable form ~f = hy, x + ez, yezi. Consider the surface s given by (cid:16) x. 2(cid:17)2 z 0. (a) compute the line integral ic. ~f d~r where the path c is the boundary of the surface s. = 1 for (b) verify your result in part (a) using a di erent method. If you can"t write d"oh! (c) verify your results in parts (a) and (b) using a di erent method. Solution: (a) ~r(t) = h2 cos t, 3 sin t, 0i, ~r (t) = h 2 sin t, 3 cos t, 0i. ~f (~r(t)) ~r (t)dt h3 sin t, 2 cos t + e0, 3 sin te0i h 2 sin t, 3 cos t, 0idt. 0 6 sin2 t + 6 cos2 t + 3 cos tdt.
