MATH 241 Study Guide - Midterm Guide: Divergence Theorem, Cylindrical Coordinate System
10 Jan 2019
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Math 241h - exam 4 - may 7, 2007 - solutions: the force eld is conservative with potential function f (x, y, z) = xy sin z + y2. The curve has initial point r(0) = (1, 1, 0) and terminal point r(1) = ( 1, e, /2). Thus the work integral is equal to f ( 1, e, /2) f (1, 1, 0) = e + e2 1: kr (t)k = 14 so rc(xy + z) ds = r 1. 0 (t(3t) + 2t + 3) 14 dt = 5 14: using green"s theorem the work integral is equal to. 2 dydx = 8/3: using divergence theorem (with a minus sign since normals are inward instead of outward) and setting up the triple integral in cylindrical coordinates, the ux integral is equal to. Is the graph of the function z = 5 x 3y with fx = 1 and fy = 3.
