Find the Volume of the Solid Generated by Revolving the Region

question 12

Short Answer

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated axis. $$y = x ^ { 2 } , \mathrm { y } = 0 , x = 3 , x = 5 \text {; the } x \text {-axis }$$

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Definitions:

Subculture

A segment of the wider society that holds distinct opinions or practices diverging from the majority's cultural standards.

Rationalization

The process of replacing traditional and emotional thought patterns with more goal-oriented, efficient, and logical ones, often associated with the development of bureaucracies and industrialization.

Counterculture

A social group whose values, beliefs, and lifestyle are in opposition to those of the main culture prevailing in a society.

Mini-culture

A smaller, distinct culture within a larger culture, characterized by unique traditions, values, or norms that differentiate it from the broader society.