MATH 2E Study Guide - Midterm Guide: Pentagon
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Solution. (a) let x = a cos t, y = a sin t, for t [0, 2 ]. 0 (b) let d be the domain enclosed by c. let p = A sin t( a sin t)dt + a2 cos2 tdt a2. Y x2 + y2 , q = x x2 + y2 . X y2 x2 (x2 + y2)2 , Y y2 x2 (x2 + y2)2 = 1: (a)find a function f such that (b) evaluate the line integralr. F = f(x, y, z) = (y2 + 4xz)i + (2xy + 2yz)j + (y2 + 2x2)k. C f dr, where c is the line segment from (1,0,-2) to (4,0,3). = y2 + 4xz implies f (x, y, z) =r (y2 + 4xz)dx + g(y, z) = xy2 + 2zx2 + g(x, y). = 2yz g(y, z) =r 2yzdy + h(z) = zy2 + h(z). Thus f (x, y, z) = xy2 + 2x2z + h(z) and.
