quiz_07C - Z 1-1 Z 2-2 f ( x,y ) dy dx = Z 1-1 Z 2-2 ± 1-x...

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Math 213 — Quiz 7 Name 1. Find the volume of the solid lying under the elliptic paraboloid x 2 / 4 + y 2 / 9 + z = 1 and above the rectangle R = [ - 1 , 1] × [ - 2 , 2]. We are asked to find the volume below the graph of the function f ( x,y ) = 1 - x 2 / 4 - y 2 / 9 above the rectangle R . So the volume is given by the integral RR R f ( x,y ) dA . We choose to evaluate this as the iterated integral
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Unformatted text preview: Z 1-1 Z 2-2 f ( x,y ) dy dx = Z 1-1 Z 2-2 ± 1-x 2 4-y 2 9 ² dy dx For the inside integral, Z 2-2 ± 1-x 2 4-y 2 9 ² dy = ³ y-y x 2 4-y 3 27 ´ 2 y =-2 = 92 27-x 2 . For the outside integral, Z 1-1 ± 92 27-x 2 ² dx = ³ 92 27 x-x 3 3 ´ 1 y =-1 = 166 27 ....
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This note was uploaded on 05/09/2008 for the course MATH 2130 taught by Professor Dorais during the Spring '08 term at Cornell.

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