matlabmontecarlonumerical-integration

How to use monte carlo method in matlab?

I need to verify that pi = integral from 0 to 2 of(sqrt(4-x^2))dx using the monte carlo method and 10^7 random numbers. I am a little confused about how to implement this in matlab. Could someone help me out?

Solution

  • The integral describes a quarter of a circle. To calculate pi follow the steps:

    1. Generate 10 ^ 7 points with coordinates (x, y) in [0 2] x [0 2]
    2. Count the points with the property that x ^ 2 + y ^ 2 <= 4. Let n be their count.
    3. Calculate the pi value: pi = 4 * n / 10 ^ 7