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13 Nov 2019
NAME: /ke Writeup #3 : Vector Fields and Line Integrals MA3160, T. Olson, Fall 2017 Answer question 1 on the back of this sheet, then complete problem 2 below on sep sheets of paper. Staple your writeup of problem 2 to the back of this sheet (trim edges if necessary). 2. Evaluate each of the following line integrals in two ways / ui(z, y)=(cos y + 1)i-xsin y J. and C1 is the straight-line path from (-5,0) to (0,4) (a) tr. dr. Where 2(r, y) (r - y)it (r y) and C2 is a circle of radius 4 centered at the origin. (b) /·U2 . dr, where C2 traversed once counterclockwise starting at (4,0). Acceptable ways to evaluate the integral: . Directly: Parametrize the path and write the integral in terms of your parametrizat . Using the Fundamental Theorem of Line Integrals: Write the theorem and show what you substitute for each part Using Green's Theorem: Write the theorem and show what you substitute for each part. lease show all steps in setting up the integral "by hand" (when neede ine limits of integration and/or potential functions, evaluate any derivativ roducts inside the integral). You may use technology to evaluate your integ
NAME: /ke Writeup #3 : Vector Fields and Line Integrals MA3160, T. Olson, Fall 2017 Answer question 1 on the back of this sheet, then complete problem 2 below on sep sheets of paper. Staple your writeup of problem 2 to the back of this sheet (trim edges if necessary). 2. Evaluate each of the following line integrals in two ways / ui(z, y)=(cos y + 1)i-xsin y J. and C1 is the straight-line path from (-5,0) to (0,4) (a) tr. dr. Where 2(r, y) (r - y)it (r y) and C2 is a circle of radius 4 centered at the origin. (b) /·U2 . dr, where C2 traversed once counterclockwise starting at (4,0). Acceptable ways to evaluate the integral: . Directly: Parametrize the path and write the integral in terms of your parametrizat . Using the Fundamental Theorem of Line Integrals: Write the theorem and show what you substitute for each part Using Green's Theorem: Write the theorem and show what you substitute for each part. lease show all steps in setting up the integral "by hand" (when neede ine limits of integration and/or potential functions, evaluate any derivativ roducts inside the integral). You may use technology to evaluate your integ
Keith LeannonLv2
13 Nov 2019