Aufgabe.

Seien $ \mbox{$a,\, b,\, c\, >\, 0$}$ . Bestimme das Volumen des Ellipsoids

$ \mbox{$\displaystyle K := \left\{ (x, y, z)^\text{t} \in \mathbb{R}^3 \;\l... ... \dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+\dfrac{z^2}{c^2} \leq 1 \right. \right\}. $}$

Berechne ferner $ \mbox{$\int_K f$}$ für

$ \mbox{$\displaystyle f\; :\; \mathbb{R}^3 \to \mathbb{R}\; , \;\;\; (x,y,z)^... ...to \left( \dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+\dfrac{z^2}{c^2} \right)^{1/2}. $}$