Use the Change of Variables $x = \sqrt { 2 } u - \sqrt { \frac { 2 } { 3 } } v$

question 135

Short Answer

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

---

Definitions:

National Organizations

Entities formed to pursue certain goals or address specific issues on a national level, often encompassing multiple states or regions within a country.

Urban League

An historic American civil rights organization dedicated to economic empowerment and elevating the standard of living in historically underserved urban communities.

Population

The total number of people inhabiting a particular country, area, or place.

New York

A state in the northeastern U.S., known for its cultural, financial, and media capital, New York City, which encompasses iconic sites like the Statue of Liberty, Empire State Building, and Central Park.