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) \(288 \pi\)

---

Definitions:

Piaget's Cognitive Development

A theory by Jean Piaget that outlines how children's cognitive abilities develop through four stages from infancy to adolescence, emphasizing the construction of understanding through interactions with the environment.

Assimilation

The cognitive process of fitting new information into pre-existing cognitive schemas, perceptions, and understanding.

Accommodation

The process of adjusting or adapting cognitive frameworks or behaviors to better align with external realities or requirements.

Cattell's Fluid

Refers to one aspect of Raymond Cattell's theory of intelligence, describing the capacity to solve novel problems, independent of acquired knowledge.