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February 12th, 2013, 11:31 AM   #1
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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
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February 12th, 2013, 12:34 PM   #2
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Re: Formulation of integral

Are you familiar with double integrals ?



where E is the area to integrate over [a circle of radius 1].
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February 12th, 2013, 01:28 PM   #3
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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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