Use the Given Transformation to Evaluate the Integral $$\begin{array} { l } x = 5 u , y = 8 v , z = 9 w \\\quad \int _ { R } \iint x ^ { 2 } y ^ { 2 } z ^ { 2 } d x d y d z\end{array}$$

question 200

Multiple Choice

Use the given transformation to evaluate the integral.
- $$\begin{array} { l } x = 5 u , y = 8 v , z = 9 w \\\quad \int _ { R } \iint x ^ { 2 } y ^ { 2 } z ^ { 2 } d x d y d z\end{array}$$
where $R$ is the interior of the ellipsoid $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 64 } + \frac { z ^ { 2 } } { 81 } = 1$

• A) \(\frac { 48 } { 7 } \pi\)
• B) \(\frac { 96 } { 7 } \pi\)
• C) \(\frac { 32 } { 21 } \pi\)
• D) \(\frac { 16 } { 21 } \pi\)