integrate method

@override ({List<double> guesses, double result}) integrate()

Calculates the numerical value of the definite function integral between lowerBound and upperBound. Returns a Record object whose members are:

• a guesses named field, which contains the list of values generated by the algorithm on each step;

• a result named field, which contains the evaluation of the integral in the [a, b] interval.

Implementation

@override
({List<double> guesses, double result}) integrate() {
  // The 'step' of the algorithm.
  final h = (upperBound - lowerBound) / intervals;

  // The initial approximation of the result.
  var integralResult =
      evaluateFunction(lowerBound) + evaluateFunction(upperBound);

  // The list containing the various guesses of the algorithm.
  final guesses = List<double>.filled(intervals, 0);

  // The actual algorithm.
  for (var i = 0; i < intervals; ++i) {
    final x = lowerBound + i * h;

    integralResult += 2 * evaluateFunction(x);
    guesses[i] = integralResult;
  }

  return (
    guesses: guesses,
    result: integralResult * h / 2,
  );
}