simpsons-rule-approximate-integration

Simpson's Rule - Approximate Integration

An integral:

$$\int_{a}^{b}f(x)dx$$

can be approximated by the so-called Simpson’s rule:

$$\dfrac{b-a}{3n}(f(a)+f(b)+4\sum_{i=1}^{n/2}f(a+(2i-1)h)+2\sum_{i=1}^{n/2-1}f(a+2ih))$$

Here h = (b - a) / n, n being an even integer and a <= b.

We want to try Simpson's rule with the function f:

$$f(x) = \frac{3}{2}\sin(x)^3$$

The task is to write a function called simpson with parameter n which returns the value of the integral of f on the interval [0, pi] (pi being 3.14159265359...).

Notes:

• Don't round or truncate your results. See in "RUN EXAMPLES" the function assertFuzzyEquals or testing.
• n will always be even.
• We know that the exact value of the integral of f on the given interval is 2.
• Please ask before translating.