#!/usr/bin/env node
 
n = Number(process.argv[2]);
 
let intv = [0, 1/2];
 
function fn(x) {
  return Math.log(4 * x * x + 1);
}
 
function Fn(x) {
  return x * Math.log(4 * x * x + 1) + Math.atan(2 * x) - 2 * x;
}
 
let approx = trapezoid_approx(fn, intv, n);
let exact = Fn(1/2) - Fn(0);
 
console.log("近似値: " + approx);
console.log("厳密値: " + exact);
 
function range(start, end) {
    return (new Array(end - start + 1)).fill(undefined).map((_, i) => i + start);
}
 
function trapezoid_approx(f, intv, n){
  let a = intv[0], b = intv[1];
  return ((b - a) / n) * ((f(a) + f(b)) / 2 + range(1, n - 1).reduce(
    (accumulator, k) => accumulator + f(a + k * (b - a) / n),
    0
  ));
}

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