Project 12.1 ? Monte Carlo Integration

question 63

Essay

Project 12.1 ? Monte Carlo Integration
A common application of Monte Carlo simulation is to provide numerical approximations.One such application is to approximate the area under a curve,or Monte Carlo integration.The following figure represents such a curve,defined over the range of X = 0 to X = 13.Call the area under this curve A.
Monte Carlo integration begins by overlaying on the curve of interest a region call this region,B)whose area is easy to calculate i.e. ,a box).Monte Carlo integration then involves the random generation of points in B and a determination of the percentage of these points that fall in A i.e. ,fall below the curve).This percentage represents that portion of the area of B that is the area of A.
Use Monte Carlo integration techniques to approximate the area under the curve.Use exact techniques to calculate the true area under the curve.How accurate is your approximation?

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Definitions:

Chronic Pain

A persistent or recurring pain that lasts longer than three months, often significantly affecting an individual’s quality of life.

Acute Pain

Short-term pain that results from tissue damage or other trauma.

Psychosocial

Referring to the interrelation of social factors and individual thought and behavior.

Gate Control Theory

A theory proposing that there are neural "gates" in the spinal cord that control the transmission of pain signals to the brain.