Volume of an ellipsoid

Well, I have a small problem. I know the general formula for the volume of an ellipsoid. But I have a task to find it with the help of an integral. Can you explain me how to do this?

 

Thank you very much, the information is great.
And can you write the formula like in https://www.physicsforums.com/showpost.php?p=577097&postcount=12" but for an ellipsoid where a, b and c are different.

 

And can you please show me how we can receive this
[tex]V = \frac{4}{3}\pi abc[/tex]
from this
[tex]2c\int_{x=-a}^a\int_{y=-b\sqrt{1-\frac{x^2}{a^2}}}^{b\sqrt{1-\frac{x^2}{a^2}}}\sqrt{1-\frac{x^2}{a^2}-\frac{y^2}{b^2}}dydx[/tex]

And can we also use http://libraryofmath.com/math/Calcu...ple_Calculus_III_Volume_of_an_Ellipsoid.html" method?