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Unformatted text preview: 2 + y 2 1. 2. Calculate Z 1 Z 1 x 2 / 3 x cos( y 4 ) dy dx. 3. Calculate Z 1 Z 1y 2 ( x 2 + y 2 ) 2003 dx dy. 4. Find the area of the region enclosed by the curve x 2 + xy + y 2 = 1 . Hint: use the substitution x = u + v 3 , y = uv 3 . 5. Let C be a plane curve starting at (0 , 0) and ending at (1 , 1). Let F = x 2 + y, y 2 + x . (a) Show that R C F d r has the same value for every C as above. (b) Compute R C F d r for a curve C as above. 6. Calculate R C F d r , where C is the unit circle oriented counterclockwise, and F is the following vector eld in the plane: F = y 3 + sin(sin x ) , x 3 + sin(sin y ) ....
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 Spring '07
 Hutchings
 Math

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