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February 10th, 2014, 07:48 PM  #1 
Newbie Joined: Feb 2014 Posts: 5 Thanks: 0  Find the average value of the function F(x,y,z) = x^2y^2z^2
I know it has something to do with arc length and I know how to find arc length for the curve, but I am confused the average value part. Thanks. 
February 11th, 2014, 02:38 AM  #2 
Senior Member Joined: Dec 2013 From: some subspace Posts: 212 Thanks: 72 Math Focus: real analysis, vector analysis, numerical analysis, discrete mathematics  Re: Find the average value of the function F(x,y,z) = x^2y^2
In 1D the average value of a function f(x) is defined by Can you see how this is generalized for 3D? 
February 11th, 2014, 04:52 AM  #3  
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: Find the average value of the function F(x,y,z) = x^2y^2 Quote:
 
February 11th, 2014, 07:42 AM  #4 
Newbie Joined: Feb 2014 Posts: 5 Thanks: 0  Re: Find the average value of the function F(x,y,z) = x^2y^2
Whoops the limits of integration for the curve were 0 to 3qrt2.

February 12th, 2014, 04:42 PM  #5 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: Find the average value of the function F(x,y,z) = x^2y^2
Your function has three variables so just saying "0 to makes no sense. Which variable is "0 to "? Or are x, y, and z give by some parametric functions with the parameter from 0 to ?


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