import math

def f(x):
    return math.sqrt(0.2*x)*math.cos(0.02*x)

def left_rect(fx: list, dx: float):
    s = 0.0
    for i in range(0, len(fx)-1):
        s += fx[i]
    return s*dx

def right_rect(xi: list, dx: float):
    return 0
    s = 0.0
    for i in range(1, len(fx)-1):
        s += fx[i]
    return s*dx

def trapezoid(xi: list, dx: float):
    return 0
    s = 0.0
    for i in range(0, len(fx)-2):
        s += (fx[i]+fx[i+1])/2
    return s*dx

def simpson(xi: list, dx: float):
    return 0
    s = 0.0
    for x in xi:
        s += dx/6 * ( f(x) + 4*f(x+dx/2) + f(x+dx) )
    return s*dx

iterations = [4,20,100,400]
xmin = 1
xmax = 3

print('\n\tleft\t\tright\t\ttrapezoid\tsimpson')
fx = []
for i in range(len(iterations)):
    fx.clear
    n = iterations[i]
    dx = (xmax - xmin)/n
    x = xmin
    for i in range(n+1):
        fx.append(f(x))
        x += dx

    #print(left_rect(fx,dx))
    #print(n,' --- ',xi)
    print(f'n={n}\t{left_rect(fx,dx):.10f}\t{right_rect(fx,dx):.10f}\t{trapezoid(fx,dx):.10f}\t{simpson(fx,dx):.10f}')