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**Unformatted text preview: **2 x y z + over the volume in the first octant bounded by the surfaces z = y + 2, x 2 + y 2 = 4, x = 0, y = 0, z = 0. Step 1 – Draw V Step 2 – contribution of a point: ( ) ( ) 2 3 2 , , cos sin x y z dzdydx f x y z dzdydx r z rdzdrd θ + = = + Step 3 – contribution of a column in the direction: 2 sin 3 2 cos sin r dl r z rdzdrd + = + ∫ Step 4 – contribution of all columns CIVE 221 Fall 2009 Nov 20 th , 2009 3 of 1 ( ) ( ) 2 sin 2 2 sin 3 2 cos sin cos sin r D D r D V dl r r z rdzdrd V r z rdzdrd θ + + = = + = + ∫∫ ∫∫∫ ∫∫∫ Step 5 – draw D Step 6 – Set up bounds of D /2 2 2 sin 3 2 cos sin r V r z rdzdrd π + = + ∫ ∫∫...

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- Fall '13
- gracie
- Multiple integral