Find the Volume of the Solid Generated by Revolving the Region

question 66

Essay

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated line. Sketch the region and a representative rectangle.
$y = \sqrt { x - 1 } , y = x - 1 ;$ the line $x = 2$

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Definitions:

Wheel Installation

The process of fitting and securing a wheel to the hub of a vehicle, ensuring it is safely and correctly attached.

Rolling Radius

The effective radius of a wheel or tire, representing the distance from the wheel center to the ground, impacting vehicle dynamics.

Tape Measure

A flexible ruler used to measure distance, typically made from a ribbon of cloth, plastic, or metal.