# -*- coding: utf-8 -*-
"""
Created on Sun Sep  4 14:18:14 2022

@author: Chris

Lab 6, Q5
"""

import numpy as np
import matplotlib.pyplot as plt
from scipy.special import p_roots

def f(x):
    f = np.cos(x)*np.exp(-2*x) 
    return f
    

for n in range(1,12):
    # set up zeros and weights
    [xj,wj]=p_roots(n)
    
    a = 1
    b = 3
    
    I = (b-a)/2*sum(wj*f((b-a)/2*xj+(b+a)/2))
    print(n,I)