April 2nd, 2015, 09:39 AM  #1 
Newbie Joined: Apr 2015 From: South Carolina Posts: 2 Thanks: 0  Triple Integral
My question isn't how to solve the triple integral, it's how to properly set it up so that it can be solved. Here is the original question: Triple Integral E (6xy) dV where E lies under the plane z = 1+x+y and above the region in the xyplane bounded by the curves y = sqrt(x), y = 0 and x = 1. I understand how to get: 0<x<1 0<y<sqrt(x) 0<z<(1+x+y) What I don't understand is how I should recognize the order in which the function is integrated. The correct way for this problem is to first integrate with respect to z then to y and finally to x. What about the wording of the problem should indicate to me that it is integrated that order as opposed to, for example, first x then z and finally y? Any help is greatly appreciated. 
April 2nd, 2015, 01:04 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,305 Thanks: 525 
By inspecting the limits. z range depends on x and y, so it has to be done first. Similarly y range depends on x, so it has to be done next.

April 2nd, 2015, 01:25 PM  #3 
Newbie Joined: Apr 2015 From: South Carolina Posts: 2 Thanks: 0 
Oh, ok. Thanks for the simple explanation!

April 2nd, 2015, 09:10 PM  #4 
Senior Member Joined: Sep 2007 From: USA Posts: 349 Thanks: 67 Math Focus: Calculus 
The order of integration can be changed, but care must be taken with the limits of integration. You would need to examine the region and adjust the limits accordingly.


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