reorder triple integralStewart Calculus 8e. 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pysches out the 4 faces of this solid, but confirm the various paramtrizations using the 2d diagrams below.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Now the various 6 triple integrals over this solid.z first: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Find the intersection of ceiling and left side wall, projected to x z plane, by eliminating y from the pair of equations to get a direct relationship between x and z.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 first: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x first: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 did these in my head, but how to distinguish from guessing or having messed up? We absolutely need the supporting diagrams for the outer double integral.
z-first, project down to the x-y plane.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x-first, project to the y-z plane.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-first, project to the x-z plane.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