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) \(27 \pi\)

Comprehend methods and measures for tracking and predicting species extinction.

Identify the role of habitat in species survival and the effects of habitat loss and degradation.

Grasp concepts related to the recovery and decline of species populations.

Analyze the effectiveness of conservation efforts and protection statuses on species survival.