Der-Int

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

double h, H, acc,  delta, X[100], Y[100], derY1[100], derY2[100], derAppY1[100], derAppY2[100], pogr1[100], pogr2[100], inSredn, inTrap, inX[100], inY[100];
int i, j, k, m, step, tochnost;

void main(void)
{
    const a=4;
    const b=7;

    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' defferencsirovaniya: \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; //kol-vo otrezkov
    for (i=0; i<=k; i++)
    {
        X[i]=a+i*h;
        Y[i]=exp(X[i])/pow(X[i],3)-pow(sin(X[i]),3);
    }

    //nachojdenie pervoi proizvodnoi
    for (i=0; i<=k; i++)
    {
        derY1[i]=(exp(X[i])*(X[i]-3)-3*pow(X[i],4)*pow(sin(X[i]),2)*cos(X[i]))/pow(X[i],4);
    }
    derAppY1[0]=-(3*Y[0]-4*Y[1]+Y[2])/(2*h); //nachalo intervala
    derAppY1[k]=(Y[k-2]-4*Y[k-1]+3*Y[k])/(2*h); //konecs intervala
    for (i=1; i<=k; i++)
    {
        derAppY1[i]=(Y[i+1]-Y[i-2])/(2*h);
    }

    //nachojdenie vtoroi proizvodnoi
    for (i=0; i<=k; i++)
    {
        derY2[i]=(3*pow(X[i],5)*pow(sin(X[i]),3)-6*pow(X[i],5)*sin(X[i])*pow(cos(X[i]),2)+exp(X[i])*(pow(X[i],2)-6*X[i]+12))/pow(X[i],5);
    }
    for (i=1; i<k; i++)
    {
        derAppY2[i]=(Y[i-1]-2*Y[i]+Y[i+1])/(h*h);
    }
    //pogreshnost'
    for (i=0; i<=k; i++)
    {
        pogr1[i]=fabs(fabs(derY1[i])-fabs(derAppY1[i]));
        pogr2[i]=fabs(fabs(derY2[i])-fabs(derAppY2[i]));
    }
    //vivod tablicsi
    printf("X\tY\tdY\tDY\tpogr\td2Y\tD2Y\tpogr\n");
    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",X[i],Y[i],derY1[i],derAppY1[i],pogr1[i],derY2[i],derAppY2[i],pogr2[i]);
    }
//=========================================================|
//==Integrirovanie--fynkcsii===============================|
//=========================================================|
    //formyla_srednich
    m=20;
    inSredn=inTrap=0;
    do
    {
        H=double(b-a)/m;
        for (i=0; i<m; i++)
        {
            inX[i]=a+i*H;
            inY[i]=exp(inX[i])/pow(inX[i],3)-pow(sin(inX[i]),3);
        }
        for (i=1; i<=m; i++)
        {
            inSredn+=H*((inY[i]+inY[i-1])/2);
        }
        inTrap=H*(inY[0]+inY[m])/2;
        for (i=1; i<m-1; i++)
        {
            inTrap+=H*inY[i];
        }
        //cout<<inTrap<<"  "<<inSredn;
        m=2*m;
        cout<<inSredn<<" "<<inTrap<<endl;
        acc=fabs(fabs(inSredn)-fabs(inTrap));
    }
    while(acc>=delta);
    cout<<m<<"  "<<H<<endl;
}