(a) Suppose that C is a simple, closed curve that does not enclose the origin. Use
Chapter 6, Problem 22(choose chapter or problem)
(a) Suppose that C is a simple, closed curve that does not enclose the origin. Use Greens theorem to determine the value of C x dx + y dy x 2 + y2 . (b) Now suppose that C is a simple, closed curve that does enclose the origin. Can you use Greens theorem to determine the value of C x dx + y dy x 2 + y2 ? Explain. (c) Let C1 and C2 be two simple, closed curves that both enclose the origin, are both oriented counterclockwise, and do not touch or intersect. Show that C1 x dx + y dy x 2 + y2 = C2 x dx + y dy x 2 + y2 . (d) Use the result of part (c) to determine the value of C x dx + y dy x 2 + y2 , where C is a simple, closed curve that encloses the origin.
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