Use the Method of Cylindrical Shells to Find the Volume $$y = x ^ { 2 } , y = 0 , x = 1 , x = 6 ; \text { about } x = 1$$

question 64

Short Answer

Use the method of cylindrical shells to find the volume of solid obtained by rotating the region bounded by the given curves about the specified axis.
$$y = x ^ { 2 } , y = 0 , x = 1 , x = 6 ; \text { about } x = 1$$

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Definitions:

Ruffini Corpuscles

Sensory receptors located in the skin that detect stretch, pressure, and warmth, playing a role in the sensation of touch and control of finger position.

Merkel Cells

Specialized cells found in the skin that are involved in the sense of touch, particularly in detecting pressure and texture.

Receptive Field

The specific area within the visual world that elicits a response from any sensory neuron.

Lamellated Corpuscles

Pressure receptors in the skin and other organs that respond to deep pressure and vibration.