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

question 243

Multiple Choice

Use the given transformation to evaluate the integral.
- $$\begin{array} { l } x = 6 u , y = 9 \mathrm { v } , z = 2 w ; \\\quad \iiint \left( \frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 81 } + \frac { z ^ { 2 } } { 4 } \right) ^ { 3 } d x d y\end{array}$$
where $R$ is the interior of the ellipsoid $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 81 } + \frac { z ^ { 2 } } { 4 } = 1$

• A) \(36 \pi\)
• B) \(81 \pi\)
• C) \(72 \pi\)
• D) \(27 \pi\)

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