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Unformatted text preview: cos(3 x 2 ) dxdy 5 4.(15 points) A lamina occupies the region inside the circle x 2 + y 2 = 2 y but outside the circle x 2 + y 2 = 1. Find the center of mass if the density at any point ( x,y ) is ρ ( x,y ) = 3 √ x 2 + y 2 6 5.(20 points) Use the transformation x = u v ,y = v to evaluate Z Z R xydA, where R is the region in the ﬁrst quadrant bounded by the lines y = x and y = 3 x and the hyperbolas xy = 1 and xy = 3. 7 6.(15 points) Find the volume of the solid that lies within the sphere x 2 + y 2 + z 2 = 4, above the xyplane and below the cone z = p 3 x 2 + 3 y 2 ....
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This note was uploaded on 05/01/2008 for the course MATH 32B taught by Professor Rogawski during the Winter '08 term at UCLA.
 Winter '08
 Rogawski
 Math

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