take the integral of a function in rust

To take the integral of a function in Rust, you can use numerical integration techniques. One popular method is the trapezoidal rule, which approximates the area under a function by dividing it into trapezoids.

Here's a Rust function that implements the trapezoidal rule:

main.rs
fn integrate(f: fn(f64) -> f64, a: f64, b: f64, n: usize) -> f64 {
    let h = (b - a) / n as f64;
    let mut sum = 0.5 * (f(a) + f(b));
    for i in 1..n {
        let x = a + i as f64 * h;
        sum += f(x);
    }
    h * sum
}
233 chars
10 lines

This function takes as input a function f that maps a f64 input to a f64 output, the limits of integration a and b, and the number of trapezoids to use n. It returns an approximation of the integral of f over the interval [a, b].

To use this function, you can define your function f as a closure or a regular function:

main.rs
let f = |x| x.sin();
let a = 0.0;
let b = std::f64::consts::PI;
let n = 1000;
let result = integrate(f, a, b, n);
println!("The integral of sin(x) from 0 to PI is {}", result);
177 chars
7 lines

This code will print out the result of integrating sin(x) from 0 to PI. You can adjust the value of n to increase the accuracy of the result, but be aware that increasing n can also significantly increase the runtime of the function.