Численное интегрирование методом Монте-Карло

4.1 Теоретический материал:

В этом методе несколько раз берётся значение подынтегральной функции от случайной величины, которая лежит между пределами интегрирования. Затем сумма полученных значений делится на объём выборки, который также называется количеством разыгрываемых точек.

4.2 Блок-схема:

Рисунок 7 – Метод Монте-Карло.

4.3 Результат работы:

Рисунок 8 – Результат вычисления методом Монте-Карло.

Листинг программы:

using System;

using System.Collections.Generic;

using System.ComponentModel;

using System.Data;

using System.Drawing;

using System.Text;

using System.Windows.Forms;

using System.Threading;

namespace nelin_ur

{

public partial class Form1: Form

{

public Form1()

{

InitializeComponent();

}

private double a = 0.0;

private double b = 1.0;

private double h, x, s;

private int n;

private double fun(double x)

{

double f = (double)(Math.Cos(x * x));

return (f);

}

private double m1(double a, double b, int n)

{

h = (b - a) / n;

x = a + h / 2;

s = 0;

for (int i = 0; i < n; i++)

{

s = s + fun(x);

x = x + h;

}

s = s * h;

return (s);

}

private double m1_gr(double a, double b, int n)

{

System.Drawing.Graphics g = System.Drawing.Graphics.FromHwnd(tabPage1.Handle);

System.Drawing.Brush brush = System.Drawing.Brushes.Red;

System.Drawing.Brush brush2 = System.Drawing.Brushes.White;

int milSec = hScrollBar1.Maximum + 10 - hScrollBar1.Value;

g.FillEllipse(brush, 201, 21, 99, 18);

g.DrawString("начало", this.Font, Brushes.Black, 230, 22);

Thread.Sleep(milSec);

g.FillEllipse(brush2, 201, 21, 99, 18);

g.DrawString("начало", this.Font, Brushes.Black, 230, 22);

g.FillRectangle(brush, 201, 51, 99, 19);

g.DrawString("ввод a,b,N", this.Font, Brushes.Black, 220, 52);

Thread.Sleep(milSec);

g.FillRectangle(brush2, 201, 51, 99, 19);

g.DrawString("ввод a,b,N", this.Font, Brushes.Black, 220, 52);

g.FillRectangle(brush, 201, 81, 99, 39);

g.DrawString("h=(b-a)/N\nx:=a;s:=0", this.Font, Brushes.Black, 223, 88);

Thread.Sleep(milSec);

g.FillRectangle(brush2, 201, 81, 99, 39);

g.DrawString("h=(b-a)/N\nx:=a;s:=0", this.Font, Brushes.Black, 223, 88);

h = (b - a) / n;

x = a;

s = 0;

for (int i = 1; i < n; i++)

{

g.FillRectangle(brush, 201, 131, 99, 19);

g.DrawString("i=1,N,1", this.Font, Brushes.Black, 225, 132);

Thread.Sleep(milSec);

g.FillRectangle(brush2, 201, 131, 99, 19);

g.DrawString("i=1,N,1", this.Font, Brushes.Black, 225, 132);

g.FillRectangle(brush, 201, 161, 99, 29);

g.DrawString("s:=s+f(x)\nx:=x+h", this.Font, Brushes.Black, 223, 162);

Thread.Sleep(milSec);

g.FillRectangle(brush2, 201, 161, 99, 29);

g.DrawString("s:=s+f(x)\nx:=x+h", this.Font, Brushes.Black, 223, 162);

x = x + h;

s = s + fun(x);

}

g.FillRectangle(brush, 201, 131, 99, 19);

g.DrawString("i=1,N,1", this.Font, Brushes.Black, 225, 132);

Thread.Sleep(milSec);

g.FillRectangle(brush2, 201, 131, 99, 19);

g.DrawString("i=1,N,1", this.Font, Brushes.Black, 225, 132);

g.FillRectangle(brush, 316, 131, 99, 19);

g.DrawString("s:=s*h", this.Font, Brushes.Black, 345, 132);

Thread.Sleep(milSec);

g.FillRectangle(brush2, 316, 131, 99, 19);

g.DrawString("s:=s*h", this.Font, Brushes.Black, 345, 132);

s = s * h;

g.FillRectangle(brush, 316, 161, 99, 19);

g.DrawString("вывод s", this.Font, Brushes.Black, 340, 162);

Thread.Sleep(milSec);

g.FillRectangle(brush2, 316, 161, 99, 19);

g.DrawString("вывод s", this.Font, Brushes.Black, 340, 162);

g.FillEllipse(brush, 316, 191, 99, 18);

g.DrawString("конец", this.Font, Brushes.Black, 345, 192);

Thread.Sleep(milSec);

g.FillEllipse(brush2, 316, 191, 99, 18);

g.DrawString("конец", this.Font, Brushes.Black, 345, 192);

return (s);

}

private double m2(double a, double b, int n)

{

double f;

h = (b - a) / n;

x = a+h;

s = 0;

s = (fun(a) + fun(b)) / 2;

for (int i = 0; i < n-1; i++)

{

s = s + fun(x);

x = x + h;

}

s = s * h;

return (s);

}

private double m2_gr(double a, double b, int n)

{

System.Drawing.Graphics g = System.Drawing.Graphics.FromHwnd(tabPage2.Handle);

System.Drawing.Brush brush = System.Drawing.Brushes.Red;

System.Drawing.Brush brush2 = System.Drawing.Brushes.White;

int milSec = hScrollBar2.Maximum + 10 - hScrollBar2.Value;

g.FillEllipse(brush, 201, 21, 99, 18);

g.DrawString("начало", this.Font, Brushes.Black, 230, 22);

Thread.Sleep(milSec);

g.FillEllipse(brush2, 201, 21, 99, 18);

g.DrawString("начало", this.Font, Brushes.Black, 230, 22);

g.FillRectangle(brush, 201, 51, 99, 19);

g.DrawString("ввод a,b,N", this.Font, Brushes.Black, 220, 52);

Thread.Sleep(milSec);

g.FillRectangle(brush2, 201, 51, 99, 19);

g.DrawString("ввод a,b,N", this.Font, Brushes.Black, 220, 52);

g.FillRectangle(brush, 201, 81, 99, 39);

g.DrawString("h=(b-a)/N\nx:=a;s:=0\ns:=(f(a)+f(b))/2", this.Font, Brushes.Black, 217, 82);

Thread.Sleep(milSec);

g.FillRectangle(brush2, 201, 81, 99, 39);

g.DrawString("h=(b-a)/N\nx:=a;s:=0\ns:=(f(a)+f(b))/2", this.Font, Brushes.Black, 217, 82);

h = (b - a) / n;

x = a;

s = 0;

s = (fun(a) + fun(b)) / 2;

for (int i = 0; i < n; i++)

{

g.FillRectangle(brush, 201, 131, 99, 19);

g.DrawString("i=1,N,1", this.Font, Brushes.Black, 225, 132);

Thread.Sleep(milSec);

g.FillRectangle(brush2, 201, 131, 99, 19);

g.DrawString("i=1,N,1", this.Font, Brushes.Black, 225, 132);

g.FillRectangle(brush, 201, 161, 99, 29);

g.DrawString("s:=s+f(x)\nx:=x+h", this.Font, Brushes.Black, 223, 162);

Thread.Sleep(milSec);

g.FillRectangle(brush2, 201, 161, 99, 29);

g.DrawString("s:=s+f(x)\nx:=x+h", this.Font, Brushes.Black, 223, 162);

s = s + fun(x);

x = x + h;

}

g.FillRectangle(brush, 201, 131, 99, 19);

g.DrawString("i=1,N,1", this.Font, Brushes.Black, 225, 132);

Thread.Sleep(milSec);

g.FillRectangle(brush2, 201, 131, 99, 19);

g.DrawString("i=1,N,1", this.Font, Brushes.Black, 225, 132);

g.FillRectangle(brush, 316, 131, 99, 19);

g.DrawString("s:=s*h", this.Font, Brushes.Black, 345, 132);

Thread.Sleep(milSec);

g.FillRectangle(brush2, 316, 131, 99, 19);

g.DrawString("s:=s*h", this.Font, Brushes.Black, 345, 132);

s = s * h;

g.FillRectangle(brush, 316, 161, 99, 19);

g.DrawString("вывод s", this.Font, Brushes.Black, 340, 162);

Thread.Sleep(milSec);

g.FillRectangle(brush2, 316, 161, 99, 19);

g.DrawString("вывод s", this.Font, Brushes.Black, 340, 162);

g.FillEllipse(brush, 316, 191, 99, 18);

g.DrawString("конец", this.Font, Brushes.Black, 345, 192);

Thread.Sleep(milSec);

g.FillEllipse(brush2, 316, 191, 99, 18);

g.DrawString("конец", this.Font, Brushes.Black, 345, 192);

return (s);

}

private double m3(double a, double b, int n)

{

double x0;

h = (b - a) / n;

x = a;

s = fun(a);

for (int i = 1; i <= n; i = i + 2)

{

x = x + h;

s = s + 4 * fun(x);

if ((i + 1) == n) break;

x = x + h;

s = s + 2 * fun(x);

};

x = b;

s = s + fun(x);

s = s * h / 3;

return (s);

}

private double m3_gr(double a, double b, int n)

{

System.Drawing.Graphics g = System.Drawing.Graphics.FromHwnd(tabPage3.Handle);

System.Drawing.Brush brush = System.Drawing.Brushes.Red;

System.Drawing.Brush brush2 = System.Drawing.Brushes.White;

int milSec = hScrollBar3.Maximum + 10 - hScrollBar3.Value;

g.FillEllipse(brush, 201, 21, 99, 18);

g.DrawString("начало", this.Font, Brushes.Black, 230, 22);

Thread.Sleep(milSec);

g.FillEllipse(brush2, 201, 21, 99, 18);

g.DrawString("начало", this.Font, Brushes.Black, 230, 22);

g.FillRectangle(brush, 201, 51, 99, 19);

g.DrawString("ввод a,b,N", this.Font, Brushes.Black, 220, 52);

Thread.Sleep(milSec);

g.FillRectangle(brush2, 201, 51, 99, 19);

g.DrawString("ввод a,b,N", this.Font, Brushes.Black, 220, 52);

g.FillRectangle(brush, 201, 81, 99, 39);

g.DrawString("h=(b-a)/N\nx:=a;s:=f(a)", this.Font, Brushes.Black, 217, 88);

Thread.Sleep(milSec);

g.FillRectangle(brush2, 201, 81, 99, 39);

g.DrawString("h=(b-a)/N\nx:=a;s:=f(a)", this.Font, Brushes.Black, 217, 88);

h = (b - a) / n;

x = a;

s = fun(a);

for (int i = 1; i <= n; i = i + 2)

{

g.FillRectangle(brush, 201, 131, 99, 19);

g.DrawString("i=1,N,1", this.Font, Brushes.Black, 225, 132);

Thread.Sleep(milSec);

g.FillRectangle(brush2, 201, 131, 99, 19);

g.DrawString("i=1,N,1", this.Font, Brushes.Black, 225, 132);

g.FillRectangle(brush, 201, 161, 99, 29);

g.DrawString("x:=x+h\ns:=s+4f(x)", this.Font, Brushes.Black, 223, 162);

Thread.Sleep(milSec);

g.FillRectangle(brush2, 201, 161, 99, 29);

g.DrawString("x:=x+h\ns:=s+4f(x)", this.Font, Brushes.Black, 223, 162);

x = x + h;

s = s + 4 * fun(x);

g.FillRectangle(brush, 201, 201, 99, 19);

g.DrawString("(i+1)==N", this.Font, Brushes.Black, 223, 202);

Thread.Sleep(milSec);

g.FillRectangle(brush2, 201, 201, 99, 19);

g.DrawString("(i+1)==N", this.Font, Brushes.Black, 223, 202);

if ((i + 1) == n) break;

g.FillRectangle(brush, 131, 231, 99, 29);

g.DrawString("x:=x+h\ns:=s+2f(x)", this.Font, Brushes.Black, 153, 232);

Thread.Sleep(milSec);

g.FillRectangle(brush2, 131, 231, 99, 29);

g.DrawString("x:=x+h\ns:=s+2f(x)", this.Font, Brushes.Black, 153, 232);

x = x + h;

s = s + 2 * fun(x);

};

g.FillRectangle(brush, 271, 231, 99, 39);

g.DrawString("x:=b\ns:=s+f(x)\ns=s*h/3", this.Font, Brushes.Black, 293, 232);

Thread.Sleep(milSec);

g.FillRectangle(brush2, 271, 231, 99, 39);

g.DrawString("x:=b\ns:=s+f(x)\ns=s*h/3", this.Font, Brushes.Black, 293, 232);

x = b;

s = s + fun(x);

s = s * h / 3;

g.FillRectangle(brush, 271, 281, 99, 19);

g.DrawString("вывод s", this.Font, Brushes.Black, 290, 282);

Thread.Sleep(milSec);

g.FillRectangle(brush2, 271, 281, 99, 19);

g.DrawString("вывод s", this.Font, Brushes.Black, 290, 282);

g.FillEllipse(brush, 271, 311, 99, 18);

g.DrawString("конец", this.Font, Brushes.Black, 305, 312);

Thread.Sleep(milSec);

g.FillEllipse(brush2, 271, 311, 99, 18);

g.DrawString("конец", this.Font, Brushes.Black, 305, 312);

return (s);

}

private Random rand = new Random();

private double m4(double a, double b, int n)

{

s = 0;

for (int i = 1; i <= n; i++)

{ s = s + fun(rand.NextDouble() * (b - a) + a); };

s = s / n;

return (s);

}

private double m4_gr(double a, double b, int n)

{

System.Drawing.Graphics g = System.Drawing.Graphics.FromHwnd(tabPage4.Handle);

System.Drawing.Brush brush = System.Drawing.Brushes.Red;

System.Drawing.Brush brush2 = System.Drawing.Brushes.White;

int milSec = hScrollBar4.Maximum + 10 - hScrollBar4.Value;

g.FillEllipse(brush, 201, 21, 99, 18);

g.DrawString("начало", this.Font, Brushes.Black, 230, 22);

Thread.Sleep(milSec);

g.FillEllipse(brush2, 201, 21, 99, 18);

g.DrawString("начало", this.Font, Brushes.Black, 230, 22);

g.FillRectangle(brush, 201, 51, 99, 19);

g.DrawString("ввод a,b,N", this.Font, Brushes.Black, 220, 52);

Thread.Sleep(milSec);

g.FillRectangle(brush2, 201, 51, 99, 19);

g.DrawString("ввод a,b,N", this.Font, Brushes.Black, 220, 52);

s = 0;

for (int i = 1; i <= n; i++)

{

g.FillRectangle(brush, 201, 81, 99, 19);

g.DrawString("i=1,N,1", this.Font, Brushes.Black, 223, 82);

Thread.Sleep(milSec);

g.FillRectangle(brush2, 201, 81, 99, 19);

g.DrawString("i=1,N,1", this.Font, Brushes.Black, 223, 82);

g.FillRectangle(brush, 201, 111, 99, 19);

g.DrawString("s:=s+f(random())", this.Font, Brushes.Black, 215, 112);

Thread.Sleep(milSec);

g.FillRectangle(brush2, 201, 111, 99, 19);

g.DrawString("s:=s+f(random())", this.Font, Brushes.Black, 215, 112);

s = s + fun(rand.NextDouble() * (b - a) + a);

};

g.FillRectangle(brush, 201, 81, 99, 19);

g.DrawString("i=1,N,1", this.Font, Brushes.Black, 223, 82);

Thread.Sleep(milSec);

g.FillRectangle(brush2, 201, 81, 99, 19);

g.DrawString("i=1,N,1", this.Font, Brushes.Black, 223, 82);

s = s / n;

g.FillRectangle(brush, 311, 81, 99, 19);

g.DrawString("s:=s/N", this.Font, Brushes.Black, 333, 82);

Thread.Sleep(milSec);

g.FillRectangle(brush2, 311, 81, 99, 19);

g.DrawString("s:=s/N", this.Font, Brushes.Black, 333, 82);

g.FillRectangle(brush, 311, 111, 99, 19);

g.DrawString("вывод s", this.Font, Brushes.Black, 330, 112);

Thread.Sleep(milSec);

g.FillRectangle(brush2, 311, 111, 99, 19);

g.DrawString("вывод s", this.Font, Brushes.Black, 330, 112);

g.FillEllipse(brush, 311, 141, 99, 18);

g.DrawString("конец", this.Font, Brushes.Black, 340, 142);

Thread.Sleep(milSec);

g.FillEllipse(brush2, 311, 141, 99, 18);

g.DrawString("конец", this.Font, Brushes.Black, 340, 142);

return (s);

}

private void Form1_Load(object sender, EventArgs e)

{

}

private void button1_Click (object sender, EventArgs e)

{

System.Drawing.Pen myPen = System.Drawing.Pens.Black;

System.Drawing.Graphics g = System.Drawing.Graphics.FromHwnd(tabPage1.Handle);

g.DrawEllipse(myPen, 200, 20, 100, 20);

g.DrawString("начало", this.Font, Brushes.Black, 230, 22);

g.DrawLine(myPen, 250, 40, 250, 50);

g.DrawRectangle(myPen, 200, 50, 100, 20);

g.DrawString("ввод a,b,N", this.Font, Brushes.Black, 220, 52);

g.DrawLine(myPen, 250, 70, 250, 80);

g.DrawRectangle(myPen, 200, 80, 100, 40);

g.DrawString("h=(b-a)/N\nx:=a;s:=0", this.Font, Brushes.Black, 223, 88);

g.DrawLine(myPen, 250, 120, 250, 130);

g.DrawRectangle(myPen, 200, 130, 100, 20);

g.DrawString("i=1,N,1", this.Font, Brushes.Black, 225, 132);

g.DrawLine(myPen, 250, 150, 250, 160);

g.DrawRectangle(myPen, 200, 160, 100, 30);

g.DrawString("s:=s+f(x)\nx:=x+h", this.Font, Brushes.Black, 223, 162);

g.DrawLine(myPen, 200, 175, 185, 175);

g.DrawLine(myPen, 185, 175, 185, 140);

g.DrawLine(myPen, 200, 140, 185, 140);

g.DrawLine(myPen, 300, 140, 315, 140);

g.DrawRectangle(myPen, 315, 130, 100, 20);

g.DrawString("s:=s*h", this.Font, Brushes.Black, 345, 132);

g.DrawLine(myPen, 365, 150, 365, 160);

g.DrawRectangle(myPen, 315, 160, 100, 20);

g.DrawString("вывод s", this.Font, Brushes.Black, 340, 162);

g.DrawLine(myPen, 365, 180, 365, 190);

g.DrawEllipse(myPen, 315, 190, 100, 20);

g.DrawString("конец", this.Font, Brushes.Black, 345, 192);

label1.Text = "";

n = 4;

s = m1_gr(a, b, n);

label1.Text = label1.Text + s + ", N=4" + "\n";

n = 10;

s = m1(a, b, n);

label1.Text = label1.Text + s + ", N=10" + "\n";

n = 50;

s = m1(a, b, n);

label1.Text = label1.Text + s + ", N=50" + "\n";

n = 500;

s = m1(a, b, n);

label1.Text = label1.Text + s + ", N=500" + "\n";

}

private void button2_Click (object sender, EventArgs e)

{

System.Drawing.Pen myPen = System.Drawing.Pens.Black;

System.Drawing.Graphics g = System.Drawing.Graphics.FromHwnd(tabPage2.Handle);

g.DrawEllipse(myPen, 200, 20, 100, 20);

g.DrawString("начало", this.Font, Brushes.Black, 230, 22);

g.DrawLine(myPen, 250, 40, 250, 50);

g.DrawRectangle(myPen, 200, 50, 100, 20);

g.DrawString("ввод a,b,N", this.Font, Brushes.Black, 220, 52);

g.DrawLine(myPen, 250, 70, 250, 80);

g.DrawRectangle(myPen, 200, 80, 100, 40);

g.DrawString("h=(b-a)/N\nx:=a;s:=0\ns:=(f(a)+f(b))/2", this.Font, Brushes.Black, 217, 82);

g.DrawLine(myPen, 250, 120, 250, 130);

g.DrawRectangle(myPen, 200, 130, 100, 20);

g.DrawString("i=1,N,1", this.Font, Brushes.Black, 225, 132);

g.DrawLine(myPen, 250, 150, 250, 160);

g.DrawRectangle(myPen, 200, 160, 100, 30);

g.DrawString("s:=s+f(x)\nx:=x+h", this.Font, Brushes.Black, 223, 162);

g.DrawLine(myPen, 200, 175, 185, 175);

g.DrawLine(myPen, 185, 175, 185, 140);

g.DrawLine(myPen, 200, 140, 185, 140);

g.DrawLine(myPen, 300, 140, 315, 140);

g.DrawRectangle(myPen, 315, 130, 100, 20);

g.DrawString("s:=s*h", this.Font, Brushes.Black, 345, 132);

g.DrawLine(myPen, 365, 150, 365, 160);

g.DrawRectangle(myPen, 315, 160, 100, 20);

g.DrawString("вывод s", this.Font, Brushes.Black, 340, 162);

g.DrawLine(myPen, 365, 180, 365, 190);

g.DrawEllipse(myPen, 315, 190, 100, 20);

g.DrawString("конец", this.Font, Brushes.Black, 345, 192);

label2.Text = "";

n = 4;

s = m2_gr(a, b, n);

label2.Text = label2.Text + s + ", N=4" + "\n";

n = 10;

s = m2(a, b, n);

label2.Text = label2.Text + s + ", N=10" + "\n";

n = 50;

s = m2(a, b, n);

label2.Text = label2.Text + s + ", N=50" + "\n";

n = 500;

s = m2(a, b, n);

label2.Text = label2.Text + s + ", N=500" + "\n";

}

private void button3_Click (object sender, EventArgs e)

{

System.Drawing.Pen myPen = System.Drawing.Pens.Black;

System.Drawing.Graphics g = System.Drawing.Graphics.FromHwnd(tabPage3.Handle);

g.DrawEllipse(myPen, 200, 20, 100, 20);

g.DrawString("начало", this.Font, Brushes.Black, 230, 22);

g.DrawLine(myPen, 250, 40, 250, 50);

g.DrawRectangle(myPen, 200, 50, 100, 20);

g.DrawString("ввод a,b,N", this.Font, Brushes.Black, 220, 52);

g.DrawLine(myPen, 250, 70, 250, 80);

g.DrawRectangle(myPen, 200, 80, 100, 40);

g.DrawString("h=(b-a)/N\nx:=a;s:=f(a)", this.Font, Brushes.Black, 217, 88);

g.DrawLine(myPen, 250, 120, 250, 130);

g.DrawRectangle(myPen, 200, 130, 100, 20);

g.DrawString("i=1,N,2", this.Font, Brushes.Black, 225, 132);

g.DrawLine(myPen, 250, 150, 250, 160);

g.DrawRectangle(myPen, 200, 160, 100, 30);

g.DrawString("x:=x+h\ns:=s+4f(x)", this.Font, Brushes.Black, 223, 162);

g.DrawLine(myPen, 250, 190, 250, 200);

g.DrawRectangle(myPen, 200, 200, 100, 20);

g.DrawString("(i+1)==N", this.Font, Brushes.Black, 223, 202);

g.DrawLine(myPen, 200, 210, 180, 210);

g.DrawLine(myPen, 180, 210, 180, 230);

g.DrawRectangle(myPen, 130, 230, 100, 30);

g.DrawString("x:=x+h\ns:=s+2f(x)", this.Font, Brushes.Black, 153, 232);

g.DrawLine(myPen, 130, 245, 125, 245);

g.DrawLine(myPen, 125, 245, 125, 140);

g.DrawLine(myPen, 125, 140, 200, 140);

g.DrawLine(myPen, 300, 140, 320, 140);

g.DrawLine(myPen, 300, 210, 320, 210);

g.DrawLine(myPen, 320, 140, 320, 230);

g.DrawRectangle(myPen, 270, 230, 100, 40);

g.DrawString("x:=b\ns:=s+f(x)\ns=s*h/3", this.Font, Brushes.Black, 293, 232);

g.DrawLine(myPen, 320, 270, 320, 280);

g.DrawRectangle(myPen, 270, 280, 100, 20);

g.DrawString("вывод s", this.Font, Brushes.Black, 290, 282);

g.DrawLine(myPen, 320, 300, 320, 310);

g.DrawEllipse(myPen, 270, 310, 100, 20);

g.DrawString("конец", this.Font, Brushes.Black, 305, 312);

label3.Text = "";

n = 4;

s = m3_gr(a, b, n);

label3.Text = label3.Text + s + ", N=4" + "\n";

n = 10;

s = m3(a, b, n);

label3.Text = label3.Text + s + ", N=10" + "\n";

n = 50;

s = m3(a, b, n);

label3.Text = label3.Text + s + ", N=50" + "\n";

n = 500;

s = m3(a, b, n);

label3.Text = label3.Text + s + ", N=500" + "\n";

}

private void button4_Click (object sender, EventArgs e)

{

System.Drawing.Pen myPen = System.Drawing.Pens.Black;

System.Drawing.Graphics g = System.Drawing.Graphics.FromHwnd(tabPage4.Handle);

g.DrawEllipse(myPen, 200, 20, 100, 20);

g.DrawString("начало", this.Font, Brushes.Black, 230, 22);

g.DrawLine(myPen, 250, 40, 250, 50);

g.DrawRectangle(myPen, 200, 50, 100, 20);

g.DrawString("ввод a,b,N", this.Font, Brushes.Black, 220, 52);

g.DrawLine(myPen, 250, 70, 250, 80);

g.DrawRectangle(myPen, 200, 80, 100, 20);

g.DrawString("i=1,N,1", this.Font, Brushes.Black, 223, 82);

g.DrawLine(myPen, 250, 100, 250, 110);

g.DrawRectangle(myPen, 200, 110, 100, 20);

g.DrawString("s:=s+f(random())", this.Font, Brushes.Black, 215, 112);

g.DrawLine(myPen, 200, 120, 180, 120);

g.DrawLine(myPen, 200, 90, 180, 90);

g.DrawLine(myPen, 180, 90, 180, 120);

g.DrawLine(myPen, 300, 90, 310, 90);

g.DrawRectangle(myPen, 310, 80, 100, 20);

g.DrawString("s:=s/N", this.Font, Brushes.Black, 333, 82);

g.DrawLine(myPen, 360, 100, 360, 110);

g.DrawRectangle(myPen, 310, 110, 100, 20);

g.DrawString("вывод s", this.Font, Brushes.Black, 330, 112);

g.DrawLine(myPen, 360, 130, 360, 140);

g.DrawEllipse(myPen, 310, 140, 100, 20);

g.DrawString("конец", this.Font, Brushes.Black, 340, 142);

label4.Text = "";

n = 4;

s = m4_gr(a, b, n);

label4.Text = label4.Text + s + ", N=4" + "\n";

n = 10;

s = m4(a, b, n);

label4.Text = label4.Text + s + ", N=10" + "\n";

n = 50;

s = m4(a, b, n);

label4.Text = label4.Text + s + ", N=50" + "\n";

n = 500;

s = m4(a, b, n);

label4.Text = label4.Text + s + ", N=500" + "\n";

}

private void tabPage1_Click(object sender, EventArgs e)

{

}

}

}

Заключение

В ходе выполнения данной лабораторной работы были изучены 4 метода численного интегрирования. Было создано приложение, демонстрирующее изученные методы на примере конкретной функции.

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