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Unformatted text preview: i 1 b i 1 √ y cos(2 π y x 2 ) + y dx B dy 4 Problem 4 Calculate the center of mass of a thin plate which has the shape of a triangle in the x, yplane given by the corners (0 ,1), (1 , 0), (0 , 1) and which has a mass density distribution given by ρ ( x, y ) = 2 x 2 . Recall that the coordinates of the center of mass are given by the Frst moments divided by the total mass. 5 Problem 5 Calculate the integral of the function i i D 3 dxdy Here the domain D is given in the new coordinates u, v by ≤ u ≤ 1 ≤ v ≤ u where u, v are deFned by the equations x = u + u 3 y = u + v + v 3 6 Problem 6 Find the surface area of the part of the paraboloid z = x 2 + y 2 that lies under the plane z = 4. The solution involves a root of 17 which you do not have to calculate. 7...
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 Winter '10
 Corbin
 #, following integral, 50 Minutes, midpoint rule Riemann

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