February 12th, 2013, 11:31 AM  #1 
Newbie Joined: Feb 2013 Posts: 21 Thanks: 0  Formulation of integral
I need to formulate the following integral from first principle and evaluate it : volume of an ellipsoid described by equation x^2 + y^2 + (z^2)/4 = 1 
February 12th, 2013, 12:34 PM  #2 
Math Team Joined: Aug 2012 From: Sana'a , Yemen Posts: 1,177 Thanks: 44 Math Focus: Theory of analytic functions  Re: Formulation of integral
Are you familiar with double integrals ? where E is the area to integrate over [a circle of radius 1]. 
February 12th, 2013, 01:28 PM  #3 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: Formulation of integral
The first thing you have to do is decide on the order of integration you want to use. If you choose to use, say "", then note that the smallest and largest possible values of x occur when y= z= 0: so x= 1 and x= 1: . Now, for each x, the largest and smallest values of y occur when z= 0: so and : . Finally, for each x and y, so : . Of course, that first integral and gives the double integral zaidalyafey gives. 

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