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

#define PI 3.14159265

/* kolme yhden muuttujan funktiota. useamman muuttujan
funktioille olisi kirjoitettava omat derivoimis- ja integroimis-
funktionsa */
double f1(double);
double f2(double);
double f3(double);

double deriv(double (*f)(double),double x,double h);
double integ(double (*f)(double),double a,double b,double h);

main()
{
	printf("f1'(1) = %g\n",deriv(&f1,1.0,0.001));
	printf("f2'(pi) = %g\n",deriv(&f2,PI,0.001));
	printf("f3'(0) = %g\n\n",deriv(&f3,0.0,0.001));

	printf("f1:n integraali yli välin [0,1] = %g\n",integ(&f1,0.0,1.0,0.001));
	/* jne. */
}

double f1(double x)
{
	return (pow(x,2.0)*sin(x));
}

double f2(double x)
{
	return (x-1.5)*(exp(-x));
}

double f3(double x)
{
	return (f1(2*x)*f2(x-4.3));
}


double deriv(double (*f)(double),double x,double h)
{
	return (f(x+h)-f(x))/h;
}

double integ(double (*f)(double),double a,double b,double h)
{
	double result;
	int i;

	for(i=0;a+i*h<b;i++)
		result += f(a+i*h);
	
	return h*result;
}