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 May 20th, 2013, 09:25 PM #1 Newbie   Joined: May 2013 Posts: 2 Thanks: 0 [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 as S 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 May 21st, 2013, 12:27 AM #2 Math Team   Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,990 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus Re: [Multivariable Calculus] Find the volume of the ellipsoi [color=#000000] and .[/color] 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? May 21st, 2013, 01:11 PM #4 Math Team   Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,990 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus 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] Tags calculus, ellipsoid, find, multivariable, volume ,
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volume of ellpiseoid by double integration

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