Determine Whether Each Integral Is Convergent or Divergent $\int _ { 3 } ^ { \infty } \frac { 1 } { x ^ { 3 / 2 } } d x$

question 60

Essay

Determine whether each integral is convergent or divergent. Evaluate those that are convergent.(a) $\int _ { 3 } ^ { \infty } \frac { 1 } { x ^ { 3 / 2 } } d x$ (b) $\int _ { e } ^ { \infty } \frac { 1 } { x ( \ln x ) } d x$ (c) $\int _ { 0 } ^ { \infty } \frac { x } { \left( x ^ { 2 } + 5 \right) ^ { 2 } } d x$

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Definitions:

Reinforcement

A process in behaviorism where a behavior becomes more likely to occur in the future due to the consequences that follow the behavior.

Matching Law

A principle stating that the proportion of responses on a particular option matches the proportion of reinforcements received for that option.

Maximizing Law

The goal of behavior in a choice task, which is to obtain as many reinforcements as possible.

Consumer Choice Behavior

Refers to the process and factors influencing the decision-making of individuals when selecting among different products or services.