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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. 

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calculating, density, shape, strange 
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