15_5_15 - 1 + 4 x 2 dx dy = Z 1 / 2 x 3 p 1 + 4 x 2 dx Z...

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15. If is the part of z = x 2 in the first octant and inside (that is, below) z = 1 - 3 x 2 - y 2 , then has projection E onto the xy -plane bounded by x 2 = 1 - 3 x 2 - y 2 , or 4 x 2 + y 2 = 1, an ellipse. Since z = x 2 has area element dS = 1 + 4 x 2 dx dy , we have ZZ xz dS = ZZ E x 3 p
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Unformatted text preview: 1 + 4 x 2 dx dy = Z 1 / 2 x 3 p 1 + 4 x 2 dx Z √ 1-4 x 2 dy = Z 1 / 2 x 3 p 1-16 x 4 dx Let u = 1-16 x 4 du = -64 x 3 dx = 1 64 Z 1 u 1 / 2 du = 1 96 ....
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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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