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Adaptive Monte Carlo Integration

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subdivisions
0
1
2
3
4
function
2
x
2
x
random seed
This Demonstration compares adaptive and nonadaptive Monte Carlo integration for two different functions,
2
x
and
2
x
. The plot shows the places on the interval
[0,2]
where sample points are added as the number of sample points is increased. The actual values of the integrals to six significant figures are 2.66667 and 5.65685. The adaptive technique generally gets better estimates with the same number of sample points by subdividing the subinterval with the highest error estimate. Normally this process would be repeated until some error criterion is satisfied, but in this Demonstration only four subdivisions are shown.
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