Der_Int_v4

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

double h, acc, H, delta, Y[100], derY1[100], derY2[100], derApp1Y[100], derApp2Y[100], pogr1[100], pogr2[100], inSredn, inTrap, inX[100], inY[100], inYsr[100], inXsr[100] ;
int i, j, k, step, tochnost;
long int m;
int a=4;
int b=7;
//======================================================|

double Function(double x)
{
    double F=0;
    F=exp(x)/pow(x,3)-pow(sin(x),3);
    return F;
}

double Derivative1(double x)
{
    double k=(b-a)/h;
    double FD1;
    FD1=(exp(x)*(x-3)-3*pow(x,4)*pow(sin(x),2)*cos(x))/pow(x,4);
    return FD1;
}

double Derivative2(double x)
{
    double k=(b-a)/h;
    double FD2;
    FD2=(3*pow(x,5)*pow(sin(x),3)-6*pow(x,5)*sin(x)*pow(cos(x),2)+exp(x)*(pow(x,2)-6*x+12))/pow(x,5);
    return FD2;
}

//======================================================|
void main(void)
{
    cout<<"Viberite shag differencsirovaniya: \n"<<"1) h=0.2\n"<<"2) h=0.1\n"<<"3) h=0.05\n";
    cin>>step;
    switch (step)
    {
    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 tochnost' integrirovaniya: \n"<<"1) delta=0.1\n"<<"2) delta=0.01\n"<<"3) delta=0.001\n";
    cin>>tochnost;
    switch (tochnost)
    {
    case 1:
        delta=0.1; break;
    case 2:
        delta=0.01; break;
    case 3:
        delta=0.001; 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]=Function(x);
    }

    //__1-ya__proizvodnaya_______________________________|
    for (i=0; i<=k; i++)
    {
        double x=a+h*i;
        derY1[i]=Derivative1(x);
    }

    derApp1Y[0]=-(3*Y[0]-4*Y[1]+Y[2])/(2*h); //nachalo intervala
    derApp1Y[k]=(Y[k-2]-4*Y[k-1]+3*Y[k])/(2*h); //konecs intervala

    for (i=1; i<k; i++)
    {
        derApp1Y[i]=(Y[i+1]-Y[i-1])/(2*h);
    }

    //__2-ya__proizvodnaya________________________________|
    for (i=0; i<=k; i++)
    {
        double x=a+h*i;
        derY2[i]=Derivative2(x);
    }

    for (i=1; i<k; i++)
    {
        derApp2Y[i]=(Y[i-1]-2*Y[i]+Y[i+1])/pow(h,2);
    }

    //__Pogreshnost'______________________________________|
    for (i=0; i<=k; i++)
    {
        pogr1[i]=fabs(fabs(derY1[i])-fabs(derApp1Y[i]));
        pogr2[i]=fabs(fabs(derY2[i])-fabs(derApp2Y[i]));
    }

    //__Vivod__Tablicsi___________________________________|
    cout<<"______________________________________________________________"<<endl;
    printf("X\tY\tder1Y\tderA1Y\tpogr1\tder2Y\tderA2Y\tpogr2\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],derY1[i],derApp1Y[i],pogr1[i],derY2[i],derApp2Y[i],pogr2[i]);
    }

//========================================================|
//=Integrirovanie--fynkcsii===============================|
//========================================================|
    m=2;
    do
    {
        inSredn=inTrap=0;
        H=double(b-a)/m;
        double x1, x2;
        for (i=1; i<=m; i++)
        {
            x1=a+H*(i-0.5);
            inSredn+=H*Function(x1);
        }

        inTrap=H*((Function(a)+Function(b))/2);
        for (i=1; i<m-1; i++)
        {
            x2=a+H*i;
            inTrap+=H*Function(x2);
        }
        m=2*m;
        acc=fabs(inTrap-inSredn);
//      cout<<"Sredn="<<inSredn<<"  "<<"Trap="<<inTrap<<endl;
    }
    while (acc>=delta);
    double inFinal=(inTrap+2*inSredn)/3;
    double pogr=fabs(6.118-inFinal);
//  cout<<m<<endl;
    cout<<"______________________________________________________________"<<endl;
    cout<<"Znachenie interala= "<<inFinal<<endl;
    cout<<"Tochnoe znachenie integrala ravno 6.118"<<endl;
    cout<<"Pogreshnost'= "<<pogr<<endl;
}