akers4 - Math 22C Exam 4 Akers - Nov 29th 00 1. (13 pts)...

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Math 22C Exam 4 Akers --- Nov 29 th 00 1. ( 13 pts ) Evaluate 2 () C x y ds where C is the second quadrant portion of the circle 22 9 xy += with counterclockwise travel. 2. ( 12 pts ) Let F x , y ( 29 = P x , y ( ˆ i + Q x , y ( j P x , y ( = 3 and ( 29 , ( 3) Qx y =- . Set up, DON’T EVALUATE , the line integral to find the work done on a particle by this force field as it travels along the parabola 2 3 yx =+ from ( 29 1,4 - to ( 29 3,12 . ( Your setup must be complete except for final integration 3. ( 13 pts ) ( 29 32 , 2, x Fx y x yexy = ++ . Find F d r C if C is the arc of the curve 3 4 4 y x = + ( 29 0,1 to 1 2, 3    . 4. ( 13 pts) F d r C 3 , 24 F x yxy is the perimeter of the rectangle with corners - 2,0 ( 29 , 2,0 ( 29 , - 2,3 ( 29 , 2,3 ( 29 with clockwise travel. 5. ( 12 pts ) Given a vector field F x , y , z ( such that ˆ ˆˆ sin x F ye i x z j yzk = +- , find: a) (5 pts) curl F :___________________________ b) (5 pts) div F :___________________________ c) (2 pts) Is F conservative?
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