Numerical Integration

The MC method for computing the area under a curve (continuous), y = f(x) from x = a to x = b is described as below:

For every run of the simulation:

{

1) Step 1: Randomly generate real numbers in the interval of [a, b]

2) Step 2: Compute the values of y for the values of x generated by Step 1

3) Step 3 : Add all the values that were computed in Step 2

}

Step 4: Compute the average value of y by dividing the sum computed in Step 3 with the total number of runs.

Step 5: The area under the curve = Value computed in Step 4 * (b – a)

Compute the area under the curve of √sin(x) using the MC method (see example below).

Example:

Monte Carlo - Area under a Curve

Input number of runs

100000

Input start of the interval - a

2

Input end of the interval - b

3.14

Area under the curve from 2.0 to 3.14 is = 0.7768