# Práctica: Integración numérica

### Objectives

During this activity, students should be able to:

• Write higher-order functions using the Python programming language.

## Activity Description

Simpson’s rule is a method for numeric integration:

$$\int_{a}^{b}f=\frac{h}{3}(y_0 + 4y_1 + 2y_2 + 4y_3 + 2y_4 + \cdots + 2y_{n-2} + 4y_{n-1} + y_n)$$

Where $$n$$ is an even positive integer (if you increment the value of $$n$$ you get a better approximation), and $$h$$ and $$y_k$$ are defined as follows:

$$h = \frac{b - a}{n}$$ $$y_k = f(a + kh)$$

Write the function integral, that takes as arguments a, b, n, and f. It returns the value of the integral, using Simpson’s rule.

Test your code with the following integrals:

$$\int_{0}^{1} x^3\textit{dx} = \frac{1}{4}$$ $$\int_{0}^{1}\frac{4}{1+x^2}\mathit{dx} = \pi$$