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 May 28th, 2017, 01:51 PM #1 Senior Member   Joined: Jan 2017 From: Toronto Posts: 209 Thanks: 3 Calculating density with strange shape... Calculate the mass of solid V bounded by given planes and having density p(x,y,z) = 3 + 2x + 2y - 2z x = 0, y = 0, z = 0, x + y = 1, z = x + 2y Answer: 1/6 May 28th, 2017, 04:03 PM #2 Senior Member   Joined: Jan 2017 From: Toronto Posts: 209 Thanks: 3 I managed to get the following boundaries... + = 1/6 Can anyone confirm the boundaries for me? Specially the first term y lower bound 1 - z? Last edited by zollen; May 28th, 2017 at 04:06 PM. May 29th, 2017, 03:11 AM #3 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 The order of your integration is awkward. We are given x = 0, y = 0, z = 0, x + y = 1, z = x + 2y. The first three say that this object is bounded by the coordinate planes- we are in the first octant. x+ y= 1 gives a boundary in the xy- plane which then extends vertically. The top is z= x+ 2y. The line x+ y= 1 goes from (1, 0) to (0, 1) so x varies from 0 to 1. For every x, y varies from 0 to 1- x. Finally, for every (x, y), z varies from 0 to x+ 2y. The integral for mass is $\displaystyle \int_0^1\int_0^{1- x}\int_0^{x+ 2y} (3 + 2x + 2y - 2z) dzdydx$ (And you are calculating the mass, not the density.) Last edited by Country Boy; May 29th, 2017 at 03:14 AM. Tags calculating, density, shape, strange 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 BurNIng Applied Math 4 July 25th, 2015 05:31 PM karans88 Probability and Statistics 7 November 13th, 2014 03:09 AM Relmiw Advanced Statistics 1 July 7th, 2013 03:05 AM alikim Calculus 0 May 22nd, 2013 08:47 PM r-soy Physics 4 February 18th, 2012 12:37 PM

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