Let’s solve Integration problems with monte carlo sampling!

Apart from the above intuitive method of deducing the value of pi simply from the shape of a circle within a square, there are other useful applications of monte carlo sampling. For instance, we can sample repeatedly to deduce the area under the graph , ie. the integral of a function.

Problem: Evaluate the definite integral of the function x^3+x^2 for -1\le x \le 1
This is shown by the area shaded in orange as shown in this image.

We can create a “box” to perform monte carlo sampling with UniformDistributionOverBox which takes in a Real Interval, with dimensions (of the cyan box) as shown in the image above

To define Polynomials in s2, we use the following
Polynomial(3.0,5.0,0.0,0.0) will define the following polymonial 


Some useful associate methods are available here :

  • To get the corresponding result when x value is placed into the polynomial, we can use .evaluate(x) where x is the corresponding x value and  is the polynomial defined earlier saved as a variable
  • We can also print the degree of polynomial (aka the power of the term with the largest effect on the outcome of the polynomial) via:
    • .degree()
  • We can get the coefficients of the various terms with :
    • .getCoefficients()[0] for instance for the first term