SecAEx3W01 - of dzdydx x y x 2 2 2 3 9 3 3- ...

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EXAM 3 MATH 22 Name: ____________________________ Winter 2001 Section: __________ You must show all work clearly to receive full credit. 1) Evaluate the iterated integrals (7) (a) cos( ) x dydx x 2 0 0 1 (7) (b) e dydx x y x 1 0 1 (12) 2) Find the volume of the solid bounded by the paraboloid and the z x y = - - 10 3 3 2 2 plane . z = 4 (14) 3) Consider a lamina that occupies the region D bounded by the parabola and x y = - 1 2 the coordinate axes in the first quadrant with density function . Find the r ( , ) x y = 2 mass m , and the center of mass of the lamina. ( , ) x y (12) 4) Set up but do not evaluate , an integral to find the area of the part of the surface that lies above the triangle with vertices , and . z x y = + 2 ( , ) 0 0 ( , ) 1 0 ( , ) 0 2 (12) 5) Convert the integral to an equivalent iterated triple integral in terms
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Unformatted text preview: of dzdydx x y x 2 2 2 3 9 3 3 +--∫ ∫ ∫ cylindrical coordinates. Do not evaluate. 6) (6) (a) Set up but do not evaluate, where E lies under the plane and dV E ∫∫∫ z y = -1 above the region in the xy-plane bounded by the curves , , and . y x = x = y = 1 (6) (b) Calculate the volume of the region E in part (a). (12) 7) Use the transformation , to set up (do not evaluate) in u x y = + v y x = -xydA R ∫∫ the uv-coordinate system where R is the square with vertices , , and . ( , ) 0 0 ( , ) 11 ( , ) 2 0 ( , ) 1 1-(12) 8) Describe the region whose area is given by the integral . rdrd q q p 1 2 3 cos ∫ ∫...
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