atmaca3 - Volume of the solid bounded by the graphs z = 9-x...

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Fall 2000 Math22 Section E and G Exam# 3 Murat atmaca 1. Evaluate the double integral of ye y 4 over the region bounded by y = x, y = 2 , and x = 0 . 2. Z 1 - 1 Z 1 - 1 Z 1 - 1 x 2 y 2 z 2 dx dy dz. 3. (SET UP DO NOT CALCULATE) Sketch the region R whose the area is given by the iterated integral. Then switch the order of integration. Z 2 0 Z x 0 dy dx + Z 4 2 Z 4 - x 0 dy dx. 4. (SET UP DO NOT CALCULATE) Find the Surface Area bounded by the cone z = p x 2 + y 2 lying inside the cylinder x 2 - 2 x + y 2 = 0. 5. (SET UP DO NOT CALCULATE) Use the Cylindrical Coordinates to evaluate Z Z Z E y dv , where E is the solid that lies the cylinders x 2 + y 2 = 1 and x 2 + y 2 = 4, above the xy-plane and below the plane z = x + 2. 6. Use a triple integral to find the
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Unformatted text preview: Volume of the solid bounded by the graphs z = 9-x 2 , y =-x + 2 , y = 0 , z = 0 and x . 7. (SET UP DO NOT CALCULATE) Find the Center of the mass of the Lamina that occupies the part of the disk x 2 + y 2 4 in the rst quadrant if the density at each point ( x,y ) is the proportional to the square of its distance between ( x,y ) and the origin. 8. Using the transformation x = u v and y = v to nd Z Z D x y dA where D is the region in the rst quadrant bounded by y = x and y = 3 x and xy = 1 and xy = 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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