Use the Given Transformation to Evaluate the Integral $\iint _ { R } ( x + y ) d A$

question 108

Short Answer

Use the given transformation to evaluate the integral.
$\iint _ { R } ( x + y ) d A$ , where $R$ is the square with vertices $( 0,0 ) , ( 4,6 ) , ( 6 , - 4 ) , ( 10,2 )$ and
$$x = 4 u + 6 v , y = 6 u - 4 v$$

---

Definitions:

Monomer Structure

The basic building block of a polymer, representing the simplest repeat unit that forms a larger chain through polymerization.

Polymer

Large molecules made up of repeating structural units known as monomers, used in a wide range of materials including plastics, textiles, and natural substances.

Monomer Unit

A small molecule that can bind chemically to other monomers to form a polymer, serving as the basic building block of polymers.

Anionic Polymerization

A type of chain-growth polymerization where the active center of the polymer chain is a negative ion.