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 December 2nd, 2012, 06:02 PM #1 Member   Joined: Dec 2010 Posts: 51 Thanks: 0 changing order of a triple integral without visual aid How would i change the order of a triple integral without a 3d rendering. For example i have: $\int_{0}^{3} \! \hspace{10 mm} \int_{0}^{2-(2y/3)} \! \hspace{10 mm} \int_{0}^{6-2y-3z} \! ze^{-x^2y^2} \, \mathrm{d} x \mathrm{d} z \mathrm{d} y$ how would i convert the order of integration to $dzdydx$? Btw, the book as the conversion as: $\int_{0}^{6} \! \hspace{10 mm} \int_{0}^{3-(x/2)} \! \hspace{10 mm} \int_{0}^{(6-x-2y)/3} \! ze^{-x^2y^2} \, \mathrm{d} z \mathrm{d} y \mathrm{d} x$
 December 3rd, 2012, 01:30 PM #2 Global Moderator   Joined: May 2007 Posts: 6,436 Thanks: 562 Re: changing order of a triple integral without visual aid You need to do it two steps, each of which requires a 2d rendering. First switch x and z. Then switch the new x and y.

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### changing order of triple integrals

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