241w-f13_15.5, 15.7-15.9

Then the triple integral of over e is suppose a solid

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Unformatted text preview: in space. Then the triple integral of over E is ∭ ∑ Suppose a solid occupies a region E in the space and its density at . Then, ∭ ∭ ̅̅ ̅ where ̅ ∭ ̅ ∭ 5 ̅ ∭ ∭ ∭ ∭ As double integrals, triple integrals can be evaluated as iterated integrals: Suppose the projection of E to the xy-plane is D, and for , if and only if Then ∭ ∬∫ . In particular, if then ∭ ∫∫∫ . 6 Examples 1. Let B be the rectangular box: Evaluate ∭ 7 2. Let E be the tetrahedron bounded by coordinate planes. Evaluate: ∭ 8 , an...
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