Use Series to Approximate the Definite Integral to Within the Indicated

question 5

Multiple Choice

Use series to approximate the definite integral to within the indicated accuracy. $$\int _ { 0 } ^ { 05 } x ^ { 2 } e ^ { - x ^ { 2 } } d x \quad \mid \text { error } \mid < 0.001$$

• A) \(0.0354\)
• B) \(0.0125\)
• C) \(0.0625\)
• D) \(0.1447\)
• E) \(0.2774\)

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Definitions:

Genetic Differences

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Dopamine

A neurotransmitter involved in many functions, including motivation, pleasure, cognition, memory, learning, and fine motor control.

Parkinson's Disease

A progressive neurological disorder characterized by motor symptoms such as tremors, stiffness, and slowed movement, caused by the loss of dopamine-producing brain cells.

Behavioral Disorder

A type of disorder that involves a pattern of disruptive behaviors in children or adults that last for at least six months and cause problems in school, at work, or in social situations.