[jbm222]

For an ellipsoid defined by the equation

(x^2)/(a^2)+(y^2)/(b^2)+(z^2)/(c^2)=1

I must find a formula giving it's volume, using triple integrals. I think i have the set up right, actually doing the intergration is extremely confusing. Does anybody know if there's some trick i can use i'm just not seeing yet?

[Role Modlin]

Originally Posted by jbm222

For an ellipsoid defined by the equation

(x^2)/(a^2)+(y^2)/(b^2)+(z^2)/(c^2)=1

I must find a formula giving it's volume, using triple integrals. I think i have the set up right, actually doing the intergration is extremely confusing. Does anybody know if there's some trick i can use i'm just not seeing yet?

When did they add letters to math?

Sorry....

[jbm222]

lol... i think around 7th grade for me.

[Mike Graham]

Do you have to do this in rectangular space? How did you set it up?

[IceHawk]

Originally Posted by Lee Modlin

When did they add letters to math?

Sorry....

Dude like algebra1 in 9th grade... are you serious?

[Visirale]

Originally Posted by IceHawk

Dude like algebra1 in 9th grade... are you serious?

Come on, get with the program, Lee!

[KATSRUS5]

if i can find my calc 3 stuff and i'll be able to help ya ...i just can't seem to find any of it right now ... and can't exactly remember how to do it ...

[theharmonicaman]

It has been a long time since I have done triple integrals, but this is how I would look at it:

(x^2)/(a^2)+(y^2)/(b^2)+(z^2)/(c^2)=1

There are only 3 variables that you are integrating, (x,y,z). The others, (a,b,c) are simply constats that define the deminsions of the elipsoid in the plane that it is associated. The fact that they are squared still makes them constants, so you can make you equation easier to look at by replacing them:

(x^2)/A+(y^2)/B+(z^2)/C=1 where A = a^2

from here the integration should be relatively strait forward... when you are integrating by x y and z should act as constants. Oh dont forget to integrate the 1.

I hope that helped... I am pretty tired at the moment.

[Mike Graham]

The way I would be apt to do it is to make it (x/a)^2+(y/b)^2+(z/c)^2=1, and then treat x/a, etc. as a variable, and integrate dV in a second, spherical transform. (I actually did it the other day to refresh myself with rectangular for the first, then a pseudo-polar parametricization.)

Remember to take the Jacobian.

If you still need help, I can scan in my work.

[SwitchfootRulz!]

yeah, what he said