Functional Riemann Sums

riemman-sum.js

const leftRiemannSum = (f, start, stop, inc) => {
  if (start >= stop) return 0;

  return f(start) * inc + leftRiemannSum(f, start + inc, stop, inc);
};

const middleRiemannSum = (f, start, stop, inc) => {
  const middle = (start + inc) / 2;
  if (start >= stop) return inc * f(middle);

  return f(middle) * inc + middleRiemannSum(f, start + inc, stop, inc);
};

const rightRiemannSum = (f, start, stop, inc) => {
  if (start >= stop) return f(stop) * inc;

  return f(stop) * inc + rightRiemannSum(f, start + inc, stop, inc);
};

const expression = n => 1 / (7 - n)

console.log("left  ", leftRiemannSum(expression, 2, 5, 1));
console.log("middle", middleRiemannSum(expression, 2, 5, 1));
console.log("right ", rightRiemannSum(expression, 2, 5, 1));