3. (Numerical Quadrature Scheme)

In Section 3.9 we developed some numerical quadrature schemes. In this exercise we extend the functionality by implementing the basic trapezoidal rule:

∫

b a

f (x)dx ≈ (b − a)

2

[f

(a) + f (b)].

Answer the following questions:

a) Implement the code for this scheme by a free function.

b) Test the code by comparing the result with the results obtained by the other methods in Section 3.9.