Use the Given Transformation to Evaluate the Integral $$\begin{array} { l } u = x + y , v = - 2 x + y ; \\\quad \int _ { R } \int _ { 2 } ( - 3 x + 4 y ) d x d y\end{array}$$

question 270

Multiple Choice

Use the given transformation to evaluate the integral.
- $$\begin{array} { l } u = x + y , v = - 2 x + y ; \\\quad \int _ { R } \int _ { 2 } ( - 3 x + 4 y ) d x d y\end{array}$$
where $R$ is the parallelogram bounded by the lines $y = - x + 1$ , $y = - x + 4 , y = 2 x + 2 , y = 2 x + 5$

• A) \(\frac { 29 } { 2 }\)
• B) 37
• C) 29
• D) \(\frac { 37 } { 2 }\)

---

Definitions:

Recent Immigrant

An individual who has moved to a new country from their country of origin relatively recently, often seeking better living conditions, employment, or safety.

Domestic Help

Employed individuals who perform a variety of household services for individuals or families from cleaning and cooking to caretaking.

Global Economy

The interconnected and interdependent nature of the world's economies, characterized by global trade, investment, and the movement of goods and services across borders.

Nation-states

Political entities consisting of a clearly defined territory and government that represents a single national identity, recognized by other states.