In the Figure Below, the Region Enclosed by the Curves $\frac { 4 } { x }$

question 122

Multiple Choice

In the figure below, the region enclosed by the curves y = - $\frac { 4 } { x }$ , y = -x, and y = -x + 3 is shown. Set up an integral or sum of integrals to find the area of the shaded region. (Do not calculate the area.)

• A) \(\int _ { - 2 } ^ { - 1 } \left( - \frac { 4 } { x } + x \right) d x\) + \(\int _ { - 1 } ^ { 2 } 3 d x\) + \(\int _ { 2 } ^ { 4 } \left( - x + 3 + \frac { 4 } { x } \right) d x\)
• B) \(\int _ { - 2 } ^ { 2 } 3 \mathrm { dx } \int _ { 2 } ^ { 4 } \left( - x + 3 - \frac { 4 } { x } \right) \mathrm { dx }\)
• C) \(\int _ { - 2 } ^ { 0 } \left( - \frac { 4 } { x } + x \right) d x\) + \(\int _ { 0 } ^ { 2 } \left( - x + 3 + \frac { 4 } { x } \right) d x\)
• D) \(\int _ { - 2 } ^ { 4 } 3 d x\)
• E) none of these

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Definitions:

Circumstantial Groups

Groups formed due to external situations or conditions rather than shared interests or goals.

Bystanders

Individuals who are present at an event or incident but do not take an active role in its outcome.

Noninterdependence

A situation or relationship where the actions, decisions, or states of one entity do not significantly affect another.

Interdependence

A mutual reliance between individuals or groups, where actions, decisions, or outcomes are influenced by others within a relationship or system.