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() {
  // Make sure to throw an exception if 'intervals' is odd.
  if (intervals % 2 != 0) {
    throw const NumericalIntegrationException(
      'There must be an even number of partitions.',
    );
  }

  // The 'step' of the algorithm.
  final h = (upperBound - lowerBound) / intervals;

  // Keeping track separately of the sums of the even and odd series.
  var oddSum = 0.0;
  var evenSum = 0.0;

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

  // The first iteration.
  for (var i = 1; i < intervals; i += 2) {
    oddSum += evaluateFunction(lowerBound + i * h);
    guesses[i] = oddSum;
  }

  // The second iteration.
  for (var i = 2; i < intervals - 1; i += 2) {
    evenSum += evaluateFunction(lowerBound + i * h);
    guesses[i] = evenSum;
  }

  // Returning the result.
  final bounds = evaluateFunction(lowerBound) + evaluateFunction(upperBound);

  return (
    guesses: guesses,
    result: (bounds + (evenSum * 2) + (oddSum * 4)) * h / 3,
  );
}