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May 20th, 2013, 09:25 PM   #1
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[Multivariable Calculus] Find the volume of the ellipsoid

Use multiple integrals, change of variables, spherical coordinates, et cetera to:

Evaluate the volume of the ellipsoid ((x^2) / 16) + ((y^2) / 9) + ((z^2) / 25) = 1

Hint : Use the volume of sphere.

I've worked through it, and have the limits of integration asS stands for integral symbol)

SS z dA Where z=f(x,y) = (plus or minus) 5 *sqrt(1-(x2)/16 - (y2))

With (-3 *sqrt(1-(x2)/16) <= y <= 3 sqrt(1-(x2)/16))

And -4 <= x <= 4
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May 21st, 2013, 12:27 AM   #2
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Re: [Multivariable Calculus] Find the volume of the ellipsoi

[color=#000000]

and



.[/color]
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May 21st, 2013, 07:59 AM   #3
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Re: [Multivariable Calculus] Find the volume of the ellipsoi

Quote:
Originally Posted by ZardoZ
[color=#000000]

and



.[/color]
Where did you get the 8 from? Was it from bring the lower bounds of the limits of integration to 0? Also, how did you determine the limits of integration in this case?
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May 21st, 2013, 01:11 PM   #4
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Re: [Multivariable Calculus] Find the volume of the ellipsoi

[color=#000000]Due to symmetry I computed the volume in the first octant and since a 3d cartesian system has 8 octants, I multiplied by 8.[/color]
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