# vcprac03 - xy plane bounded by y = x 2 x = 2 y = 0(a Sketch...

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The University of Sydney School of Mathematics and Statistics Practice Session 3 MATH2061: Vector Calculus Summer School 2012 1. Sketch the following regions: (a) { ( x, y ) R 2 | 1 x 2 , x y x } (b) { ( x, y ) R 2 | x = r cos θ, y = r sin θ, 0 θ 2 π, 1 r 2 } 2. Describe the shaded regions as sets of points in R 2 (as in question 1 ). Use polar coordinates in part (c). (a) (b) (c) y =2 x 3 y = x 2 2 y =1 - x y = x 2 3. Sketch the region of integration and then evaluate integraldisplay 2 0 integraldisplay 3 0 ( x 2) sin y dx dy . 4. Evaluate integraldisplayintegraldisplay R x 2 e x 2 + y 2 dxdy where R is the region defined by x 2 + y 2 4, y 0. 5. Let I = integraldisplayintegraldisplay R xydxdy

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Unformatted text preview: xy plane bounded by y = x 2 , x = 2, y = 0. (a) Sketch the region R . (b) Evaluate I by doing the y integral Frst. (c) Evaluate I by doing the x integral Frst. Copyright c c 2012 The University of Sydney 1 6. Evaluate c C ye x dx − 2 xy 2 dy, where C is the square with vertices at (1 , 1) , ( − 1 , 1) , ( − 1 , − 1) , (1 , − 1) . 7. Evaluate i 2 i 1 x/ 2 y 2 cos( xy ) dy dx . 2...
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