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

question 78

Multiple Choice

Use the given transformation to evaluate the integral.
- $$\begin{array} { l } x = 9 u , y = 10 v , z = 4 w ; \\\quad \int _ { R } \iint \left( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \right) d x d y d z\end{array}$$
where $R$ is the interior of the ellipsoid $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 100 } + \frac { z ^ { 2 } } { 16 } = 1$

• A) \(144 \pi\)
• B) \(216 \pi\)
• C) \(240 \pi\)
• D) \(288 \pi\)

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