# -*- coding: utf-8 -*-
"""
Created on Sun Jan 29 14:09:43 2023

@author: your mom
"""

# step 1 import necessary librairies

import numpy as np
import matplotlib.pyplot as plt

# step 2 define starting variables

xi = 0
xf = 2
npts = 21
x = np.linspace(xi,xf,npts)
f = np.zeros(npts)
g = np.zeros(npts)

# step 3 define functions that will be later plotted

for i in range(len(x)):
f = x **3
if x <=-1:
g = 3 * x + 2
elif x < 1:
g = f
else:
g = 3 * x - 2

# step 4 graph the functions previously defined

plt.plot(x,f, label = 'f(x)')
plt.plot(x,g, label = 'g(x)')
plt.legend()
plt.title("There is no title idiot")
plt.grid(True, "both", 'both')

# step 5 calculate the integral of the function g(x) between x = 0 and x = 2

A1=0
dx = x[1] - x[0]
for j in range(0,npts-1):
A1= A1 + ( g[j]+g[j+1] )/2*dx
print(f"L'intégrale de la fonction g(x) entre x=0 et x=2 est {A1:.4f}")