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#include <cstdlib>
#include <iostream.h>
#include <math.h>
#include <stdio.h>
using namespace std;
double F(double x)
{
return 2/sqrt(1-pow(x,2.0));
}
long double simpson(int n ,double a, double b)
{
long double s=0.0, h=0.0, x=0.0;
if((n/2)*2 != n) {n=n+1;}
h = (b-a)/double(n);
for ( int i=2; i<=n-1; i=i+2)
{
x = a+double(i)*h;
s = s + 2.0*F(x) + 4.0*F(x+h);
}
s = (s + F(a)+F(b)+4.0*F(a+h) )*h/3.0;
return s;
}
double trapezoid(int n, double a, double b)
{double h=0.0;
double T=0.0;
double y=0.0;
double z1=0.0;
double z2=0.0;
h=(b-a)/double(n);
z1=h*(F(a)+F(b))/2;
for(int i=1; i<=(n-1); i=(i+2))
{z2+=F(a+(h*double(i)));}
z2=h*z2;
T=z1+z2;
return T;}
double rectangle(int n, double a, double b)
{double h=0,p=0;
double y=0;
h=(b-a)/double(n);
for(int i=0; i<=(n-1);i++)
{y+=F(a+(h*double(i)));}
p=h*y;
return p;
}
double tangents(int n, double a, double b)
{double h=0,p=0;
double y=0;
h=(b-a)/double(n);
for(int i=1; i<=(n-1);i=i+2)
{y+=F(a+(h*double(i)));}
p=2*h*y;
return p;}
void choice(int n, double a, double b)
{int choice=0;
double s=0.0;
double t=0.0;
double r=0.0;
double ta=0.0;
printf("Choix de method: \n\t1 - simpson\n\t2 - trapezoid\n\t3 - rectangle\n\t4 - tangents\n\nChoix: ");
scanf("%d",&choice);
switch(choice)
{case 1:
simpson(n,a,b);
s=simpson(n,a,b);
printf("\n %lf\n",s); /* on affiche le re'sultat */
break;
case 2:
trapezoid(n,a,b);
t=trapezoid(n,a,b); /* on stock dans une variable tampon */
printf("\n %lf\n",t);
break;
case 3:
rectangle(n,a,b);
r=rectangle(n,a,b); /* on stock dans une variable tampon */
printf("\n %lf\n",r);
break;
case 4:
tangents(n,a,b);
ta=tangents(n,a,b);
printf("\n %lf\n",ta);
break;
}}
int main(int argc, char *argv[])
{ int n;
double a,b;
a=0.0; /* Borne inferieure */
b=1.0; /* Borne superieure */
n=1000; /* Nombre d'iteration */
choice(n,a,b);
system("PAUSE");
return 0;
}
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