Diferencia entre revisiones de «Elipsoide»

::<math> \int_{0}^{\pi } \int_{0}^{2\pi } \int_{0}^{1} abc\cdot r^2 sin(\theta)drd\theta d\varphi = abc \int_{0}^{1} r^2dr \int_{0}^{\pi }sin(\thetavarphi ) \int_{0}^{2\pi }d\varphidr = \!</math>

::<math>abc\cdot \left [ \frac{r^3 }{3}\right ]_{0}^{1}\cdot \left [ -cos(\thetavarphi ) \right ]_{0}^{\pi }\cdot \left [ \varphitheta \right ]_{0}^{2\pi } =abc\cdot \frac{1}{3}\cdot2\pi\cdot2 = \frac{4}{3}\pi a\ b\ c\ \!</math>