Use the Transformation $x = \sqrt { 2 } u - \sqrt { \frac { 2 } { 3 } } v , y = \sqrt { 2 } u + \sqrt { \frac { 2 } { 3 } } v$

question 43

Multiple Choice

Use the transformation $x = \sqrt { 2 } u - \sqrt { \frac { 2 } { 3 } } v , y = \sqrt { 2 } u + \sqrt { \frac { 2 } { 3 } } v$ to evaluate the integral $\iint _ { R } \left( x ^ { 2 } - x y + y ^ { 2 } \right) d A$ , where $R$ is the region bounded by the ellipse $x ^ { 2 } - x y + y ^ { 2 } = 2$ .

• A) \(\frac { 100 \pi } { 3 ^ { 3 / 2 } }\)
• B) \(\frac { 25 } { \sqrt { 3 } }\)
• C) \(\frac { 5 \pi } { \sqrt { 3 } }\)
• D) \(\frac { 5 \pi ^ { 2 } } { \sqrt { 3 } }\)
• E) \(\frac { 4 \pi } { \sqrt { 3 } }\)

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Definitions:

Homozygous

Having two identical alleles.

Allele

One of two or more alternative forms of a gene that arise by mutation and are found at the same place on a chromosome.

XYY Sex Chromosomal

Refers to a genetic condition in which a male has an extra Y chromosome, often associated with tall stature but typically without significant physical or mental disabilities.

Language Development

The way in which toddlers begin to make sense of and communicate in language throughout their early years.