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15_6_5 - 5 The part of z = a x 2 y 2 lying above z = b< a...

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Unformatted text preview: 5. The part of z = a - x 2 - y 2 lying above z = b < a lies inside the vertical cylinder x 2 + y 2 = a - b. For z = a - x 2 - y 2 , the upward vector surface element is 2xi + 2yj + k ^ N dS = d x dy. 1 Thus the flux of F = xi + yj + zk upward through ^ F N dS is = = 2 0 x 2 +y 2 a-b a-b [2(x 2 + y 2 ) + a - x 2 - y 2 ] d x dy (r 2 + a)r dr = (a - b)(3a - b). 2 d 0 = 2 a(a - b) (a - b)2 + 4 2 ...
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