SecBEx3W01 - x y that occupies the region , . r p ( , ) x y...

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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) sin( ) x y dydx + 0 2 0 2 p p (7) (b) e dxdy x y 2 1 0 1 (7) (c) x y z dzdydx sin( ) 2 2 - - - p p p p p p 2) To find the volume of the solid under the paraboloid and above the region z x y = + 2 2 bounded by and , set up but do not evaluate y x = 2 x y = 2 (8) (a) a double integral (6) (b) a triple integral (12) 3) Convert the double integral to polar coordinates. (Do not evaluate). x y dydx x x 2 2 0 2 0 2 2 + - (16) 4) Find the mass m and the center of mass of the lamina with density function ( ,
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Unformatted text preview: x y that occupies the region , . r p ( , ) x y = { D x y y x = ( , ) cos } 2 x p (10) 5) Convert the integral to an equivalent iterated triple integral in terms of 1 2 2 2 4 16 4 dzdydx x y x +- cylindrical coordinates. Do not evaluate. (12) 6) Describe the region whose area is given by the integral . rdrd q q p p 2 4 6 2 sin (15) 7) Use the transformation , to evaluate , where D is the u y x = + v y x = -e dA y x D- square with vertices , , and . ( , ) 0 2 ( , ) 2 2 ( , ) 11 ( , ) 1 3...
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This note was uploaded on 01/24/2011 for the course MATH 22 taught by Professor Brigham during the Winter '08 term at Missouri S&T.

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SecBEx3W01 - x y that occupies the region , . r p ( , ) x y...

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