make c+++ code (Monte Carlo Integration) The average value of a function f over an interval [a, b] isgiven by1favg = f(2) dz.b - aThis formula can be used to approximate an integral by approximating the averagevalue of ƒ by sampling the value of f(x) at a large number of randomly chosen pointsin [a, b] and computing the sample mean of these values. That is,N[ f(x) dz =Ni=1where the r; are chosen randomly according to a uniform distribution in the interval[a, b].Note: While this idea is actually inefficient in 1 dimension, it is a common strategyfor very high dimensional integrals and there are numerous improvements that can bemade to make it even mroe efficient.mc_int Function:Input variables:• an anonymous function representing f• a scalar representing a• a scalar representing b• a scalar representing NOutput variables:a scalar representing the value of the integralA possible sample case is:>> approx_intapprox_int = 0.99821mc_int(@(x) sin(x), 0, pi/2, 1000)%3D

(Monte Carlo Integration) The average value of a function f over an interval [a, b] is given by Savg = -a f(2) dr. This formula can be used to approximate an integral by approximating the average value of ƒ by sampling the value of f(x) at a large number of randomly chosen points in [a, b] and computing the sample mean of these values. That is, f(r) dx = N i=1

(Monte Carlo Integration) The average value of a function f over an interval [a, b] is given by Savg = -a f(2) dr. This formula can be used to approximate an integral by approximating the average value of ƒ by sampling the value of f(x) at a large number of randomly chosen points in [a, b] and computing the sample mean of these values. That is, f(r) dx = N i=1

C++ for Engineers and Scientists

4th Edition

ISBN:9781133187844

Author:Bronson, Gary J.

Publisher:Bronson, Gary J.

Chapter5: Repetition Statements

Section5.7: Do While Loops

Problem 6E: (Numerical analysis) Here’s a challenging problem for those who know a little calculus. The...

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