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Simple Monte Carlo integration

More generaly, imagine a rectangle of height in the integration interval , such that the function is within its boundaries. Compute pairs of random numbers such that they are uniformly distributed inside this rectangle. The fraction of points that fall within the area contained below , i. e., that satisfy is an estimate of the ratio o fthe integral of and the area of the rectangle. Hence, the estimate of the integral will be given by:

 (267)

Another Monte Carlo procedure is based on the definition:

 (268)

In order to determine this average, we sample the value of :

where the values are distributed unformly in the interval . The integral will be given by

Next: Monte Carlo error analysis Up: Monte Carlo integration Previous: Monte Carlo integration