Math 2E 44275 Spring 2014 Quiz 4 5 08 14 Name Print ID Number Show all of your work Partial credit will be given 1 10 points a Evaluate the line integral by using parametric equations cos ydx x2 sin ydy C is the rectangle with vertices 0 0 5 0 5 2 and 0 2 oriented counterclockwise b Evaluate the same line integral by using Green s Theorem Solution a C1 x t y 0 0 t 5 dx dt dy 0dt C2 x 5 y t 0 t 2 dx 0dt dy dt C3 x 5 t y 2 0 t 5 dx dt dy 0dt C4 x 0 y 2 t 0 t 2 dx 0dt dy dt cos ydx x2 sin ydy cos ydx x2 sin ydy I C C1 C2 C3 C4 Z 2 Z 5 1dt 0 25 cos t 2 Z 5 0 cos 2 t 5 52 sin tdt 0 0 0 t 5 cos 2dt 0dt 0 30 1 cos 2 0 Z 2 Z C I Z C b The region D enclosed by C is 0 5 0 2 so cos ydx x2 sin ydy 2x sin y sin y dydx cid 20 ZZ Z 5 0 x2 sin y y x D cos y dA sin ydy cid 2 x2 x cid 3 5 Z 2 0 2x 1 dx cid 21 Z 5 Z 2 0 0 0 cos y 2 0 30 1 cos 2
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