Implementing Numerical Integration Using Function Pointers The problem is to wri
ID: 3757692 • Letter: I
Question
Implementing Numerical Integration Using Function Pointers
The problem is to write a function “integrate” with prototype:
//FUNC represents functions of one variable that take a double as input and returns a double
typedef double (*FUNC)(double);
double integrate(FUNC f, double a, double b);
so that when it is passed a function f and bounds a and b, the call:
integrate(f, a,b) will return the value of the definite integral of f evaluated between a and b.
test integrate on the following three functions:
1. double line(double x){
return x;
{
2. double square(double x){
return x*x;
{
3. double cube(double x){
return x*x*x;
{
And the following main function:
int main(){
cout<< “The integral of f(x)=x between 1 and 5 is: “<<integrate(line, 1, 5)<<endl;
cout<< “The integral of f(x)=x^2 between 1 and 5 is: “<<integrate(square, 1, 5)<<endl;
cout<< “The integral of f(x)=x^3 between 1 and 5 is: “<<integrate(cube, 1, 5)<<endl;
}
How does integrate work?
Inside a loop we sum up the area of rectangles with a small base (say .0001) and height f(x) for each x between a and b in increments of .0001.
When the loop terminates, we return the value of the sum.
The purpose if this assignment is to see (and implement) a very simple application of function pointers.
Explanation / Answer
The sample example below :-)