text: /*
  *
  * @file
  * @title Composite Simpson's rule for definite integral evaluation
  * @author: [ggkogkou](https://github.com/ggkogkou)
  * @brief Calculate definite integrals using composite Simpson's numerical method
  *
  * @details The idea is to split the interval in an EVEN number N of intervals and use as interpolation points the xi
  * for which it applies that xi = x0 + i*h, where h is a step defined as h = (b-a)/N where a and b are the
  * first and last points of the interval of the integration [a, b].
  *
  * We create a table of the xi and their corresponding f(xi) values and we evaluate the integral by the formula:
  * I = h/3 * {f(x0) + 4*f(x1) + 2*f(x2) + ... + 2*f(xN-2) + 4*f(xN-1) + f(xN)}
  *
  * That means that the first and last indexed i f(xi) are multiplied by 1,
  * the odd indexed f(xi) by 4 and the even by 2.
  *
  * N must be even number and a<b. By increasing N, we also increase precision
  *
  * More info: [Wikipedia link](https://en.wikipedia.org/wiki/Simpson%27s_rule#Composite_Simpson's_rule)
  *
  */
  
  function integralEvaluation (N, a, b, func) {
    // Check if N is an even integer
    let isNEven = true
    if (N % 2 !== 0) isNEven = false
  
    if (!Number.isInteger(N) || Number.isNaN(a) || Number.isNaN(b)) { throw new TypeError('Expected integer N and finite a, b') }
    if (!isNEven) { throw Error('N is not an even number') }
    if (N <= 0) { throw Error('N has to be >= 2') }
  
    // Check if a < b
    if (a > b) { throw Error('a must be less or equal than b') }
    if (a === b) return 0
  
    // Calculate the step h
    const h = (b - a) / N
  
    // Find interpolation points
    let xi = a // initialize xi = x0
    const pointsArray = []
  
    // Find the sum {f(x0) + 4*f(x1) + 2*f(x2) + ... + 2*f(xN-2) + 4*f(xN-1) + f(xN)}
    let temp
    for (let i = 0; i < N + 1; i++) {
      if (i === 0 || i === N) temp = func(xi)
      else if (i % 2 === 0) temp = 2 * func(xi)
      else temp = 4 * func(xi)
  
      pointsArray.push(temp)
      xi += h
    }
  
    // Calculate the integral
    let result = h / 3
    temp = 0
    for (let i = 0; i < pointsArray.length; i++) temp += pointsArray[i]
  
    result *= temp
  
    if (Number.isNaN(result)) { throw Error("Result is NaN. The input interval doesn't belong to the functions domain") }
  
    return result
  }
  
  
  