Monte Carlo Integration Calculator
Monte Carlo Integration Calculator estimates the definite integral \\( \int_a^b f(x) \, dx \\) using Monte Carlo integration. Enter a function \\( f(x) \\) (e.g., “x^2 + 2*x + 1”), interval bounds \\( a \\) and \\( b \\), and number of samples \\( N \\). The calculator generates random samples, computes the integral estimate, and visualizes the function with sample points using p5.js. Steps are shown with MathJax.
Monte Carlo Integration Calculator
This calculator estimates the definite integral \\( \int_a^b f(x) \, dx \\) using Monte Carlo integration. Input a function \\( f(x) \\) (e.g., “x^2 + 2*x + 1”), interval bounds \\( a \\) and \\( b \\), and number of samples \\( N \\). The calculator generates random samples \\( x_i \sim \text{Uniform}(a, b) \\), computes the estimate \\( \frac{b-a}{N} \sum f(x_i) \\), and visualizes the function with sample points using p5.js. Computational steps are shown with MathJax.
Example 1: Quadratic Function
Function: \\( x^2 \\), \\( a = 0 \\), \\( b = 1 \\), \\( N = 1000 \\).
Result: Integral estimate \\( \approx 0.333 \\).
Example 2: Linear Function
Function: \\( 2x + 1 \\), \\( a = 0 \\), \\( b = 2 \\), \\( N = 1000 \\).
Result: Integral estimate \\( \approx 6 \\).
Example 3: Trigonometric Function
Function: \\( \sin(x) \\), \\( a = 0 \\), \\( b = \pi \\), \\( N = 1000 \\).
Result: Integral estimate \\( \approx 2 \\).