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 September 29th, 2018, 10:40 AM #1 Newbie   Joined: Feb 2016 From: Durham Posts: 8 Thanks: 1 How to change the order of integration in 3D? I have been working on a problem that requires me to integrate in the following way: $$\int_{0}^{\infty} \int_{0}^{y} \int_{0}^{y-x} f(x,y,z)\ dzdxdy$$ I would like to change the order of integration, with dz going last. For the dydxdz option, I've got: $$\int_{0}^{\infty} \int_{0}^{\infty} \int_{x+z}^{\infty} f(x,y,z)\ dydxdz$$ Is this correct? And what would the dxdydz option look like? Thanks in advance for any help! September 29th, 2018, 04:35 PM   #2
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 Originally Posted by db561 I have been working on a problem that requires me to integrate in the following way: $$\int_{0}^{\infty} \int_{0}^{y} \int_{0}^{y-x} f(x,y,z)\ dzdxdy$$ I would like to change the order of integration, with dz going last. For the dydxdz option, I've got: $$\int_{0}^{\infty} \int_{0}^{\infty} \int_{x+z}^{\infty} f(x,y,z)\ dydxdz$$ Is this correct? And what would the dxdydz option look like? Thanks in advance for any help!
Whether you can do this or not depends on $f$. The computations you provided aren't always valid and there is no reason to expect them to be. You have to know ahead of time that both integrals you have written are finite. In that case, then its true they are equal. Tags 3-d, calculus, change, integration, order Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post life24 Calculus 4 October 27th, 2016 11:06 AM JWS Calculus 0 May 25th, 2014 12:36 AM VFernandes Applied Math 1 January 5th, 2012 01:38 PM n757 Calculus 1 May 30th, 2011 01:41 PM poppy Calculus 1 January 4th, 2010 04:43 PM

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