private void MainForm_Load(object sender, EventArgs e)
{
// function under integral sign
Integrals.FunctionDelegate function = (x => 1 / (x * x + 5));
// upper and lower bounds for the definite interval
Interval interval = new Interval(0, 1);
// expected value of the integral of the function on interval above
double integral = Math.Atan(1 / Math.Sqrt(5)) / Math.Sqrt(5);
// supremum of under integral function's derivative of degree k
FunctionDelegate derivativeUpper = (k => Factorial(k) / Math.Pow(Math.Sqrt(5), k + 2));
// desired number of segments after interval partition
int N = 2;
labelIntegralFunction.Text = "int of 1 / (x * x + 5) on [0, 1]";
labelIntegral.Text = integral.ToString();
FillDataGrid(function, interval, integral, derivativeUpper, N);
}
private void FillDataGrid(Integrals.FunctionDelegate function, Interval interval, double integral, FunctionDelegate derivativeUpper, int N)
{
var sumNLeftTriangles = Integrals.CalculateLeftRectanglesIntegral(interval, N, function);
var sum2NLeftTriangles = Integrals.CalculateLeftRectanglesIntegral(interval, 2 * N, function);
var sumNTrapezoid = Integrals.CalcualteTrapezoidIntegral(interval, N, function);
var sum2NTrapezoid = Integrals.CalcualteTrapezoidIntegral(interval, 2 * N, function);
var sumNSimpsons = Integrals.CalculateSimpsonsIntergral(interval, N, function);
var sum2NSimpsons = Integrals.CalculateSimpsonsIntergral(interval, 2 * N, function);
var errorLeftTriangles = Integrals.GetErrorForLeftRectangles(interval, N, derivativeUpper(Integrals.DLeftRectangles + 1));
var errorTrapezoid = Integrals.GetErrorForTrapezoidIntegral(interval, N, derivativeUpper(Integrals.DTrapezoid + 1));
var errorSimpsons = Integrals.GetErrorForSimpsonsIntegral(interval, N, derivativeUpper(Integrals.DSimpsons + 1));
var error2LeftTriangles = Integrals.GetErrorForLeftRectangles(interval, 2 * N, derivativeUpper(Integrals.DLeftRectangles + 1));
var error2Trapezoid = Integrals.GetErrorForTrapezoidIntegral(interval, 2 * N, derivativeUpper(Integrals.DTrapezoid + 1));
var error2Simpsons = Integrals.GetErrorForSimpsonsIntegral(interval, 2 * N, derivativeUpper(Integrals.DSimpsons + 1));
var errorMainLeftTriangles = Integrals.GetMainErrorForLeftRectangles(sum2NLeftTriangles, sumNLeftTriangles);
var errorMainTrapezoid = Integrals.GetMainErrorForTrapezoidIntegral(sum2NTrapezoid, sumNTrapezoid);
var errorMainSimpsons = Integrals.GetMainErrorForSimpsonsIntegral(sum2NSimpsons, sumNSimpsons);
var iAdLeftTriangles = Integrals.GetAdjustedIntegral(sum2NLeftTriangles, errorMainLeftTriangles);
var iAdTrapezoid = Integrals.GetAdjustedIntegral(sum2NTrapezoid, errorMainTrapezoid);
var iAdSimpsons = Integrals.GetAdjustedIntegral(sum2NSimpsons, errorMainSimpsons);
dataGrid.Rows.Add("Left rect", sumNLeftTriangles, integral - sumNLeftTriangles, errorLeftTriangles,
sum2NLeftTriangles, integral - sum2NLeftTriangles, error2LeftTriangles,
errorMainLeftTriangles, iAdLeftTriangles, integral - iAdLeftTriangles);
dataGrid.Rows.Add("Trapezoid", sumNTrapezoid, integral - sumNTrapezoid, errorTrapezoid,
sum2NTrapezoid, integral - sum2NTrapezoid, error2Trapezoid,
errorMainTrapezoid, iAdTrapezoid, integral - iAdTrapezoid);
dataGrid.Rows.Add("Simpson", sumNSimpsons, integral - sumNSimpsons, errorSimpsons,
sum2NSimpsons, integral - sum2NSimpsons, error2Simpsons,
errorMainSimpsons, iAdSimpsons, integral - iAdSimpsons);
}
