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 February 12th, 2013, 10:31 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, 11:34 AM #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, 12:28 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. Tags formulation, integral 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 Jhenrique Calculus 0 December 4th, 2013 06:02 AM Rethki Probability and Statistics 1 December 14th, 2012 12:35 PM lalitp Algebra 1 December 12th, 2012 12:27 AM momo Number Theory 1 April 11th, 2009 09:49 PM

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