15_R_4 - Z 1-x y ( 1-x-y ) dy = √ 3 Z 1 x ( 1-x ) 3 6 dx...

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4. The plane x + y + z = 1 has area element dS = 3 dx dy . If is the part of the plane in the first octant, then the projection of on the xy -plane is the triangle 0 x 1, 0 y 1 - x . Thus ZZ xyz dS = 3 Z 1 0 x dx
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Unformatted text preview: Z 1-x y ( 1-x-y ) dy = √ 3 Z 1 x ( 1-x ) 3 6 dx Let u = 1-x du = -dx = √ 3 6 Z 1 u 3 ( 1-u ) du = √ 3 6 ± 1 4-1 5 ² = √ 3 120 ....
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This note was uploaded on 03/08/2012 for the course MATH 120 taught by Professor Onurfen during the Spring '12 term at Middle East Technical University.

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