#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Tue Feb  4 10:32:17 2020

@author: suwako
"""


def rectangle(f, a, b, n):
    h = (b - a) / n
    aire = 0
    for i in range(n):
        aire += f(a+i*h)
    return aire*h

def trapeze(f, a, b, n):
    h = (b - a) / n
    aire = 0
    for i in range(n):
        aire += (f(i*h) + f((i+1)*h))
    return aire*h/2

def milieu(f, a, b, n):
    h = (b - a) / n
    aire = 0
    for i in range(n):
        aire += f((a+h*i + a + h*(i+1))/2)
    return aire*h