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

// functions to integrate
double f1(double x){
return sqrt(x);
}

double f2(double x){
return log(x);
}

double f3(double x){
return exp(x);
}
double f4(double x){
return x*x;
}

double f5(double x){
return x*x*x;
}

double trapeze(double (*f)(double),double a, double b, int n){

double h = (b-a)/(double)n;

double x = a;
double x_next = x + h;
double A;
double I = 0;
int i;
for(i = 1; i<=n; i++){
A = (h/2) * ( f(x) + f(x_next) ); // Trapezoidal area
x = x + h;
x_next = x + h;

I = I + A; // sum up the areas to get the integral
}

return I;
}

int main(){

double a,b; // integral limits
int n; // number of points
double I1,I2,I3,I4,I5; // values for the different integrals

a = 0;
b = 1;
n = 100;

I1 = trapeze(f1,a,b,n);
I2 = trapeze(f2,a,b,n);
I3 = trapeze(f3,a,b,n);
I4 = trapeze(f4,a,b,n);
I5 = trapeze(f5,a,b,n);

printf("\nIntegral of f(x) = sqrt(x) using %d points on [%0.2f %0.2f] is %0.4f",n,a,b,I1);
a=0.01;
printf("\nIntegral of f(x) = ln(x) using %d points on [%0.2f %0.2f] is %0.4f",n,a,b,I2);
a=0;
printf("\nIntegral of f(x) = exp(x) using %d points on [%0.2f %0.2f] is %0.4f",n,a,b,I3);
printf("\nIntegral of f(x) = x^2 using %d points on [%0.2f %0.2f] is %0.4f",n,a,b,I4);
printf("\nIntegral of f(x) = x^3 using %d points on [%0.2f %0.2f] is %0.4f",n,a,b,I5);


return 0;
}