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:

Examining Table

A piece of medical equipment in clinics and hospitals where patients sit or lie down for examination by healthcare professionals.

Position

The location or orientation of an object or individual, or a particular stance on an issue or in a debate.

Lengthwise

In a direction or orientation that runs along the longest dimension of an object.

Customary Size

The typical or standard dimensions or measurements of objects based on common or traditional usage.