Simpson's Rule

Write a function of the following form:

double simpint(double f[],double r[],double dr[],int N)

Return value:

• Simpson's rule approximation to $\int_0^1 f(r(u)) \frac{dr}{du}(u)\, du= \int_{r(0)}^{r(1)} f(r) \, dr$.

Input:

• f[]: values of $f(r(u_i))$ for $i=0 \ldots N$ ( $u_i\equiv 1/N$).
• r[]: values of $r(u_i)$.
• dr[]: values of $\frac{dr}{du}(u_i)$.
• N: twice the number of integration intervals (i.e., the number the number of sample points minus one.)