Der_Int_Gayss2

#include <iostream.h>
#include <iomanip.h>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>

double h, acc, H, Y[100], dY1[100], dY2[100], dA1Y[100], dA2Y[100], pog1[100], pog2[100], inY1, inY2, Int, pogInt;
int i, k, shag, otrezki;
int m;
int a=5;
int b=8;
//======================================================|

double Fun(double x)
{
    double F=0;
    F=pow(x,0.5)-pow(cos(x),2);
    return F;
}

double D1(double x)
{
    double k=(b-a)/h;
    double Diff1;
    Diff1=1/(2*pow(x,0.5))+sin(2*x);
    return Diff1;
}

double D2(double x)
{
    double k=(b-a)/h;
    double Diff2;
    Diff2=2*cos(2*x)-1/(4*pow(x,1.5));
    return Diff2;
}

//======================================================|
void main(void)
{
    cout<<"Viberite shag differencsirovaniya: \n"<<"1) h=0.2\n"<<"2) h=0.1\n"<<"3) h=0.05\n";
    cin>>shag;
    switch (shag)
    {
    case 1:
        h=0.2; break;
    case 2:
        h=0.1; break;
    case 3:
        h=0.05; break;
    default:
        cout<<"Vibrano nevernoe znachenie!\n";
    }

    cout<<"Viberite chislo shagov integrirovaniya: \n"<<"1) m=10\n"<<"2) m=20\n"<<"3) m=40\n";
    cin>>otrezki;
    switch (otrezki)
    {
    case 1:
        m=10; break;
    case 2:
        m=20; break;
    case 3:
        m=40; break;
    default:
        cout<<"Vibrano nevernoe znachenie!\n";
    }

//==Differencsirovanie--fynkcsii========================|
    k=(b-a)/h;
    for (i=0; i<=k; i++)
    {
        double x=a+h*i;
        Y[i]=Fun(x);
    }

    //__1-ya__proizvodnaya__|
    for (i=0; i<=k; i++)
    {
        double x=a+h*i;
        dY1[i]=D1(x);
    }

    dA1Y[0]=-(3*Y[0]-4*Y[1]+Y[2])/(2*h); //nachalo intervala
    dA1Y[k]=(Y[k-2]-4*Y[k-1]+3*Y[k])/(2*h); //konecs intervala

    for (i=1; i<k; i++)
    {
        dA1Y[i]=(Y[i+1]-Y[i-1])/(2*h);
    }

    //__2-ya__proizvodnaya__|
    for (i=0; i<=k; i++)
    {
        double x=a+h*i;
        dY2[i]=D2(x);
    }

    for (i=1; i<k; i++)
    {
        dA2Y[i]=(Y[i-1]-2*Y[i]+Y[i+1])/pow(h,2);
    }

    //__Pogreshnost'__|
    for (i=0; i<=k; i++)
    {
        pog1[i]=fabs(dY1[i]-dA1Y[i]);
        pog2[i]=fabs(dY2[i]-dA2Y[i]);
    }

    //__Vivod__Tablicsi__|
    cout<<"=============================================================="<<endl;
    printf("X\tY\td1Y\tdA1Y\tpog1\td2Y\tdA2Y\tpog2\n");
    cout<<"______________________________________________________________"<<endl;
    for (i=0; i<=k; i++)
    {
        printf("%2.2f\t%4.3f\t%4.3f\t%4.3f\t%5.4f\t%4.3f\t%4.3f\t%5.4f\n",a+i*h,Y[i],dY1[i],dA1Y[i],pog1[i],dY2[i],dA2Y[i],pog2[i]);
    }

//=Integrirovanie--fynkcsii===============================|

    inY1=inY2=0;
    H=double(b-a)/m;
    double x1, x2;
    for (i=1; i<=m; i++)
    {
        x1=a+H*(i-0.5)+(h/2)*0.5773502692;
        inY1+=(H/2)*Fun(x1);
    }
    for (i=1; i<=m; i++)
    {
        x2=a+H*(i-0.5)-(h/2)*0.5773502692;
        inY1+=(H/2)*Fun(x2);
    }
    Int=inY1+inY2;
    pogInt=fabs(6.067-Int);
    cout<<"=============================================================="<<endl;
    cout<<"Znachenie integrala="<<Int<<endl;
    cout<<"Tochnoe znachenie integrala=6.067"<<endl;
    cout<<"=============================================================="<<endl;

}