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

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Definitions:

Functional Fixedness

A cognitive bias that limits a person to using an object only in the way it is traditionally used, hindering problem-solving.

Availability Heuristic

A cognitive shortcut based on the first instances that pop into someone's mind upon assessing a particular subject, idea, technique, or choice.

Functional Fixedness

A psychological inclination that constrains someone to applying an artifact only in its accepted traditional role, thereby stifling creative thought and problem resolution.

Availability Heuristic

A mental shortcut that relies on immediate examples that come to a person's mind when evaluating a specific topic, concept, method or decision.