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Homework 6 Solutions - Engineering Math Bemewerk 6...

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Unformatted text preview: Engineering Math Bemewerk 6 Solutions Spring 2010 i; = [ 252,;egez,xezj T: $2 + 22 S 4 0 g y g 10 a: R 8 z 3 0 (onequarter of a solid eyiinder) S : the complete boundary of T, ofiented with the positive direction outward ti w In order to avoid parametrizing five surfaces, use the Divergence Theorem. fffiv’ - "EMA = fffdiv‘fidv = ffoxe“ +0+ xezmv 2 fffsxezdv 3 T T T Use cylindricai coordinetes with :2: m 9“ cos 9, y = y, z = i" sin 6. Baredem 20 W52 23rcos§ersmgrdrdfldy T o a 0 .2 £2 . g . = jg 0m {)1 3r2cos66’3‘“ Edy 659 d?“ m j: (:52 [372(3036 6* may [:0] d6 d7" 2 Jr)? :59 30T200538r8in9d9d7- u m rsinB du m Tcosadfi .1f ['2 2 . , m j; [307“ 8’ SM ] dr D m f: 30r(e” — 3dr w [02 (30m? —— 30r)dr u 2 1,. dv = grew duzdr v=e’ ’3‘ 7—: (30(‘I’ST m 8’) m 15”) 6 ~_«» (6082 m 3%2 ~ 59) w (0 — 39 — 0) m 3062 —~ 30 ...
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