MAT-2130 Final: MATH 2130 App State Spring2011 Final Exam answer key
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Name: x = cos( ) sin( ) y = sin( ) sin( ) z = 2 (1 + cos(2 )) (a) let f(x, y, z) = hxy5, zx, 1i and c be the curve parameterized by r(t) = h3 cos(t), 7t, 3 sin(t)i where t 4 . Set up but do not evaluate the line integral: zc. F dr. (b) let c be the line y = 2x 1 where 1 x 2. Compute zc (y + 1) dx + x dy: (12 points) let r be the region bounded by y = 5 x2 and y = x 1 (pictured below). [warning: one of the integrals below will have to be split into 2 pieces. ] (a) set up the integral zz. 2xy da in the order of integration: dy dx . 2xy da in the order of integration: dx dy . Include a sketch of the region of integration.
