Determine Whether the Improper Integral $\int _ { 0 } ^ { \infty } x e ^ { - x / 3 } d x$

question 24

Multiple Choice

Determine whether the improper integral $\int _ { 0 } ^ { \infty } x e ^ { - x / 3 } d x$ diverges or converges. Evaluate the integral if it converges.

• A) 9
• B) \(e ^ { - 1 / 3 }\)
• C) \(- \frac { 1 } { 3 }\)
• D) 3
• E) diverges

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Definitions:

Band Society

A small, loosely organized group of hunter-gatherers who work together and share resources, usually consisting of 20-50 individuals.

State Society

A complex social organization characterized by a formal governmental structure and socioeconomic stratification.

Cultural Controls

Means of ensuring that individuals or groups conduct themselves in ways that support and maintain the established cultural order. They may be internal (ingrained sentiments about what is proper and what is not) or external (such as sanctions).

Leader of the Band

A term metaphorically used to describe the person who provides direction and guidance to a group or team, much like a conductor in a musical band.