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. $$y = \frac { 1 } { x \left( x ^ { 2 } + 144 \right) } , \quad y = 0 , x = 1 , x = 12 \text {; the } y \text {-axis }$$

---

Definitions:

Bait and Switch

A deceptive marketing strategy where a customer is lured by the advertisement of a low-priced item but then is encouraged to buy a more expensive one.

Caveat Emptor

A Latin phrase meaning "let the buyer beware," indicating that the buyer assumes the risk for the quality of goods purchased, unless protected by warranty.

Former Price Comparisons

A method of evaluating the price history of a product or service to assess its current value.

High Price Tags

Items or services being sold at a high cost, indicating either premium quality, brand value, or exclusivity.