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

question 145

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) \(\frac { 560 \pi } { \pi + 1 }\)

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