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Can you help me with this integral?

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- Thread starter -=nobody=-
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- #1

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Can you help me with this integral?

- #2

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- #3

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Should I do it like it is described in this article?

http://libraryofmath.com/math/Calcu...mple_Calculus_III_Volume_of_an_Ellipsoid.html

If I do it so u=x/a, v=y/b, w=z/c.

How can I prove that http://libraryofmath.com/math/Calcu...f_Variables_in_Multiple_Integrals_gr_136.gif" =3/4Pi*a*b*c

http://libraryofmath.com/math/Calcu...mple_Calculus_III_Volume_of_an_Ellipsoid.html

If I do it so u=x/a, v=y/b, w=z/c.

How can I prove that http://libraryofmath.com/math/Calcu...f_Variables_in_Multiple_Integrals_gr_136.gif" =3/4Pi*a*b*c

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Well, how would you go about proving that the unit ball has volume [itex]\frac{4}{3}\pi[/itex] ?

- #5

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Well, the idea is probably good, but it doesn't help me with the integral

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- #7

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Won't it be much more complicated, or is it the only way?

r=(x^2+y^2+z^2)^1/2.

r=(x^2+y^2+z^2)^1/2.

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- #9

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Sorry for this post, I had some problems with my internet browser.

- #10

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-=nobody=-, as everyone has already said on this thread, transform your coordinates. ie, set

[tex] x= a r \cos\theta [/tex]

[tex] y = b r\sin \theta [/tex]

Now, find the Jacobian and limits of integration of [itex] \theta [/itex] and [itex] r [/itex]. Can you take it from here?

[tex] x= a r \cos\theta [/tex]

[tex] y = b r\sin \theta [/tex]

Now, find the Jacobian and limits of integration of [itex] \theta [/itex] and [itex] r [/itex]. Can you take it from here?

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