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HW24-Solution - HW24 Solution Terry Cooke Cal Poly San Luis...

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HW24 - Solution Terry Cooke: Cal Poly San Luis Obispo
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Chapter 9, Solution 23 ( a ) 2 dA u du 2 2 3 (2 ) 2 O dJ u dA u u du u du 2 1 2 1 3 4 2 1 2 4 R O O R R R J dJ u du u 4 4 2 1 2 O J R R ( b ) From Eq. (9.4): ( Note by symmetry.) x y I I 4 4 2 1 2 1 2 4 O x y x x O J I I I I J R R 4 4 2 1 4 x I R R
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Chapter 9, Solution 26 The equation of the circle is 2 2 2 x y r So that 2 2 x r y Now 2 2 dA xdy r y dy Then 2 2 /2 2 r r A dA r y dy Let sin ; cos y r dy r d Then /2 2 2 /6 /2 /2 2 2 2 /6 /6 2 2 6 3 2 2 2 ( sin ) cos sin 2 2 cos 2 2 4 sin 3 2 2 2 2 4 3 8 2.5274 A r r r d r d r r r r
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