Use the Given Transformation to Evaluate the Integral Where $R$ Is the Interior of the Ellipsoid

Multiple Choice

Use the given transformation to evaluate the integral.
- $$\begin{array} { l } x = 4 u , y = 5 v , z = 7 w ; \\\quad \iiint \left( \frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 25 } + \frac { z ^ { 2 } } { 49 } \right) ^ { \pi } d x d y\end{array}$$
where $R$ is the interior of the ellipsoid $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 25 } + \frac { z ^ { 2 } } { 49 } = 1$

A) $\frac { 280 \pi } { \pi + 1 }$
B) $\frac { 560 \pi } { \pi + 2 }$
C) $\frac { 560 \pi } { \pi + 3 }$
D) $\frac { 560 \pi } { \pi + 1 }$