Use the Method of Cylindrical Shells to Find the Volume $$y = \frac { 1 } { x \left( x ^ { 2 } + 144 \right) } , \quad y = 0 , x = 1 , x = 12 \text {; the } y \text {-axis }$$

question 45

Short Answer

Use the method of cylindrical shells to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated axis.Sketch the region and a representative rectangle. $$y = \frac { 1 } { x \left( x ^ { 2 } + 144 \right) } , \quad y = 0 , x = 1 , x = 12 \text {; the } y \text {-axis }$$

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Definitions:

Natural Mimicry

The adaptation where an organism evolves to resemble another object or organism in its natural environment for survival.

Facial Feedback

The hypothesis that facial movement and expressions can influence emotional experience.

Behavior Feedback

The information received about the effectiveness or appropriateness of one's actions, which can influence future behaviors.

Gestures

Physical actions or movements, particularly of the hands or face, used to express thoughts, intentions, or feelings without using words.