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13 Nov 2019
1. Compute if C goes from (0,0) to (1,3) along the line parameterized as z-, y = 31 2. Let C be the (oriented) curve in the plane given by the graph of y = x2 froin the point (0,0) to the point (2,4) (a) Integrate f(x,y) = 2y along C (with respect to arc length) (b) Let Fr, y22yj. Integrate F along C 3. Compute the le integral along the following curves (a) Cl along the circle x2 + ya_ 1 frorn the point (1,0) to (0.1) using x = cost, y = sint (b) C2 along the line z +y = 1 froin (0.1) to (1,0). (c) C = G + C, for the curves C1 and C2 in parts (a) and (b) 4. (a) Find a function f(r,y) with gradient F, where (b) Use your solution to part (a) to evaluate where C is a curve from (0,2) to (,1) 5. Use Green's Theorem to evaluate the line integral where C is the positively oriented curve determined by y and y Include a sketch of the curve that shows the direction of the curve. from (0,0) to (4,2)
1. Compute if C goes from (0,0) to (1,3) along the line parameterized as z-, y = 31 2. Let C be the (oriented) curve in the plane given by the graph of y = x2 froin the point (0,0) to the point (2,4) (a) Integrate f(x,y) = 2y along C (with respect to arc length) (b) Let Fr, y22yj. Integrate F along C 3. Compute the le integral along the following curves (a) Cl along the circle x2 + ya_ 1 frorn the point (1,0) to (0.1) using x = cost, y = sint (b) C2 along the line z +y = 1 froin (0.1) to (1,0). (c) C = G + C, for the curves C1 and C2 in parts (a) and (b) 4. (a) Find a function f(r,y) with gradient F, where (b) Use your solution to part (a) to evaluate where C is a curve from (0,2) to (,1) 5. Use Green's Theorem to evaluate the line integral where C is the positively oriented curve determined by y and y Include a sketch of the curve that shows the direction of the curve. from (0,0) to (4,2)
Hubert KochLv2
23 Jul 2019