Areas of Curved Regions The Monte Carlo method can be used to estimate the area under the graph of a function. The figure below shows the region under the graph of , above the -axis, between and . If we choose a point in the square at random, the probability that it lies under the graph of is the area under the graph divided by the area of the square. So if we randomly select a large number of point in the square, we have
Modify the program from Problem to carry out this Monte Carlo simulation and approximate the required area.
The required area using Monte Carlo simulation.
1) The circle in the figure has radius and the square has area .
2) Choose a point at random from the square, the probability that it lies under the graph will be
3) The Monte Carlo method involves choosing many points inside the square. Then,
Modify the following program on the calculator to generate random points and approximate the required area
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