Use a Graphing Utility to (A) Plot the Graphs of the Given

question 108

Essay

Use a graphing utility to (a) plot the graphs of the given functions and (b) find the approximate $x$ -coordinates of the points of intersection of the graphs. Then find an approximation of the volume of the solid obtained by revolving the region bounded by the graphs of the functions about the $x$ -axis. Round answers to two decimal places.
$$y = \frac { 1 } { 5 } x ^ { 5 } , \mathrm { y } = 3 x ^ { 2 } - x ^ { 3 }$$

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Definitions:

Counterirritation

A method for managing pain or discomfort by intentionally inducing a second, less severe pain or irritation, to distract from the original pain.

Chronic Pain

A persistent pain that continues for weeks, months, or even years beyond the usual recovery period or occurs along with a chronic health condition.

Gate Control Theory

The proposal that pain sensations must pass through a neural “gate” in order to reach the brain and can be blocked at that gate by neurons that inhibit signals from the nociceptors.

Nocioception

The sensory nervous system's response to certain harmful or potentially harmful stimuli.