Example: Area inside a Curve (cont)
Simulation approach to determining the area:
- determine a region completely enclosing curve
- generate very many random points in this region
- for each point x, compute inside(x)
- count number of insides and outsides
- areaWithinCurve = totalArea * insides/(insides+outsides)
i.e. we approximate the area within the curve by using
the ratio of points inside the curve against those outside
This general method of approximating is known as Monte Carlo estimation.
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