Trapezoidal rule, a technique for approximating a definite integral

trapezoidal_method.py

# Numerical Analysis
# Trapezoidal Method
# Author: A.F. Agarap

# Function = SUM(i = 1, n) h / 2 (f(x[1]) + f(x[n + 1]) + 2(f(x[2]) + f(x[3]) + ... + f(x[n])))
# f(x) = cos(x**2) * exp(x**3)

import math
import os

def main():
	a = int(input("Enter value for a: "))
	b = int(input("Enter value for b: "))
	n = int(input("Enter value for n: "))
	x = generate_set(a, b, n)
	result = 0
	for i in range(0, (n + 1)):
		result += function(x[i]) if (i == 0 or i == n) else (2 * function(x[i]))
	print(result * ((abs(a - b) / n) / 2))

def generate_set(a, b, n):
	x = []
	h = abs(a - b) / n
	for i in range(n + 1):
		x.append(a + (i * h))
	return x 

def function(x):
	return math.cos(x**2) * math.exp(x**3)

main()