Matlab

20, Monte Carlo integration. One way to estimate the value of definite integrals in spaces with many dimensions is the Monte Carlo integration method. We illustrate the method here in two-dimensions. Consider the task of estimating the area of a circle of radius R Inscribe the circle in a square with sides of length 2R. To estimate the area, randomy pick N points in the square (use rand). Find how many points Nin are in the circle. The estimate for the area is then the fraction of all the points that are in the circle times the area of the square, A AMc (Nin/N)4R2. Write a program, MonteCarloCircle.m that implements this algorithm. Tabulate AMc for N- 10* where k (1,2,...,7). Make a graphical representation of the points 'raining down" on the square with points inside the circle being a different color than points outside the circle