Функція FullIntegral(aFull,bFull:real) тип real

 

 

 

                                       так                                   ні

 

 

                 так                                                        ні

 

 

 

так                                                      ні

 

 

                                     так                                                       ні

 

 

С Лiстiнг програми

 

unit funct;

 

interface

uses

Windows, Messages, SysUtils, Classes, Graphics, Controls, ExtCtrls, Math;

 

const

a = 0;

b = 6;

 

type

one_array = array of real;

Parametrs = record

nSimp, nTrap:integer;

end;

 

function y(x:real):real;

function first(x1,x2:real):real;

procedure setN(nG, nT, nS:integer);

procedure createGrid;

procedure createGridOfInt;

function integralSimpsona(aSim,bSim:real):real;

function integralTrapeciay(aTrap,bTrap:real):real;

function FullIntegral(aFull,bFull:real):real;

 

var

Xgrid:one_array;     GridOfInt:one_array;     nGrid, nSim, nTrap:integer;

 

implementation

//--------------------------------------------------------------

function y(x:real):real;

begin

Result:=2*arctan(x)-11*Power(3,(-x))+5;

end;

//--------------------------------------------------------------

function first(x1,x2:real):real;

begin

result:=5*x2+2*x2*ArcTan(x2)+11*Power(3,(-x2))/Ln(3)-Ln(1+x2*x2)-(5*x1+2*x1*ArcTan(x1)+11*Power(3,(-x1))/Ln(3)-Ln(1+x1*x1));

end;

//--------------------------------------------------------------

procedure setN(nG, nT, nS:integer);

begin

nGrid:=nG; nSim:=nS; nTrap:=nT;

end;

//--------------------------------------------------------------

procedure createGrid;

var i:integer; h:real;

begin

h:=(b-a)/nGrid;

SetLength(Xgrid,nGrid+1);

for i:=0 to nGrid do

Xgrid[i]:=a+h*i;

end;

//--------------------------------------------------------------

procedure createGridOfInt;

var i, n:integer;

begin

n:=High(Xgrid);

SetLength(GridOfInt,n+1);

for i:=1 to n do

GridOfInt[i]:=integralSimpsona(a,Xgrid[i]);

end;

//--------------------------------------------------------------

function integralSimpsona(aSim,bSim:real):real;

var X:one_array;     i:integer;     sum1, sum2, h:real;

begin

if(aSim<>bSim)then

begin

h:=(bSim-aSim)/nSim;

SetLength(X,nSim+1);

for i:=0 to nSim do

   X[i]:=aSim+h*i;

sum1:=0;

sum2:=0;

for i:=1 to (nSim div 2) do

   sum1:=sum1+y(X[2*i-1]); 

for i:=1 to ((nSim div 2)-1) do

   sum2:=sum2+y(X[2*i]);

Result:=(bSim-aSim)*(y(X[0])+y(X[nSim])+4*sum1+2*sum2)/(3*nSim);

end

else

Result:=0;

end;

//--------------------------------------------------------------

function integralTrapeciay(aTrap,bTrap:real):real;

var   i:integer;     sum, h:real;     X:one_array;

begin

h:=(bTrap-aTrap)/nTrap;

SetLength(X,nTrap+1);

for i:=0 to nTrap do

X[i]:=aTrap+h*i;

sum:=(y(X[0])+y(X[nTrap]))/2;

for i:=1 to (nTrap-1) do

    sum:=sum+y(X[i]);

Result:=sum*h;

end;

//--------------------------------------------------------------

function FullIntegral(aFull,bFull:real):real;

var        z1, z2, z3, raznost:real;     i, ai, bi:integer;

begin

if(aFull<>bFull)then

begin

for i:=0 to (High(Xgrid)-1) do

   begin

     if((Xgrid[i]<=aFull)and(aFull<=Xgrid[i+1]))then ai:=i;

     if((Xgrid[i]<=bFull)and(bFull<=Xgrid[i+1]))then bi:=i;

   end;

raznost:=GridOfInt[ai]+integralTrapeciay(Xgrid[ai],aFull);

Result:=GridOfInt[bi]+integralTrapeciay(Xgrid[bi],bFull)-raznost;

end

else

Result:=0;

end;

//--------------------------------------------------------------

end.

 

unit UnitMAIN;

interface

uses

Windows, Messages, SysUtils, Classes, Graphics, Controls, Forms, Dialogs, jpeg, ExtCtrls, StdCtrls, funct;

 

type

TForm1 = class(TForm)

Image1: TImage; Image2: TImage; Button1: TButton; Image3: TImage; Edit1: TEdit; Edit2: TEdit;

Label1: TLabel; Label2: TLabel; Label3: TLabel; Memo1: TMemo; Panel1: TPanel; Button2: TButton;

Button3: TButton; Label4: TLabel; Label5: TLabel; Label6: TLabel; Label7: TLabel; Edit3: TEdit;

Edit4: TEdit; Edit5: TEdit; Label8: TLabel;

 

procedure Button1Click(Sender: TObject);

procedure Button2Click(Sender: TObject);

procedure Button3Click(Sender: TObject);

procedure FormCreate(Sender: TObject);

end;

 

var

Form1: TForm1;

 

implementation

 

{$R *.DFM}

 

procedure TForm1.Button1Click(Sender: TObject);

var          i:integer;           intF, intS, intT, intR, L,R:real;      file1:TextFile;

begin

L:=StrToFloat(Edit1.Text);       R:=StrToFloat(Edit2.Text);

if(((0<=L)and(L<=6))and(((0<=R)and(R<=6))))

then

begin

   createGrid;

   createGridOfInt;

   intF:=FullIntegral(L,R);

   Label1.Caption:=FloatToStr(intF);

   intS:=integralSimpsona(L,R);

   intT:=integralTrapeciay(L,R);

   intR:=first(L,R);

   AssignFile(file1,'Result.txt');

   Rewrite(file1);

   writeln(file1,'Дйствительное значение интеграла       ',intR:17:15);

   writeln(file1,'Значение интеграла по формуле (1)        ',intF:17:15,' Расность по модулю ',abs(intF-intR):17:15);

   writeln(file1,'Значение интеграла по формуле трапеций ',intT:17:15,' Расность по модулю ',abs(intT-intR):17:15);

   writeln(file1,'Значение интеграла по формуле Симпсона ',intS:17:15,' Расность по модулю ',abs(intS-intR):17:15);

   CloseFile(file1);

   Memo1.Lines.LoadFromFile('Result.txt');

end

else ShowMessage('граници должна быть в пределах от 0 до 6');

 

end;

 

procedure TForm1.Button2Click(Sender: TObject);

begin

Panel1.Visible:=true;   Button2.Visible:=false;

end;

 

procedure TForm1.Button3Click(Sender: TObject);

begin

Panel1.Visible:=false;    Button2.Visible:=true;

setN(StrToInt(Edit5.Text),StrToInt(Edit3.Text),StrToInt(Edit4.Text));

end;

 

procedure TForm1.FormCreate(Sender: TObject);

begin

setN(StrToInt(Edit5.Text),StrToInt(Edit3.Text),StrToInt(Edit4.Text));

end;

end.