Use the Given Transformation to Evaluate the Integral Where $R$ Is the Parallelogram Bounded by the Lines

question 184

Multiple Choice

Use the given transformation to evaluate the integral.
- $$\begin{array} { c } \mathrm { u } = \mathrm { x } + \mathrm { y } , \mathrm { v } = - 2 \mathrm { x } + \mathrm { y } ; \\\iint _ { \mathrm { R } } 3 \mathrm { xdxdy } ,\end{array}$$
where $R$ is the parallelogram bounded by the lines $y = - x + 1 , y = - x + 4 , y = 2 x + 2 , y = 2 x + 5$

• A) 3
• B) 6
• C) -6
• D) -3

---

Definitions:

GDP Spent

The portion of the Gross Domestic Product that is used for expenditure, including consumption, investment, government spending, and net exports.

Health Care

A broad term encompassing all services, systems, or products related to maintaining or improving an individual’s health, including prevention, diagnosis, treatment, and recovery.

Rising Prices

An economic situation characterized by a general increase in the prices of goods and services over a period of time, often measured by inflation rates.

Health Care Costs

The expenses related to medical services, treatments, drugs, and other health-related items.