import numpy as np
import pylab as plt

t = np.linspace(0,2*np.pi,100)
dt = t[1] - t[0]

x = 10 * np.cos(t) + np.sin(t)
y = np.sin(t) + np.cos(t)

err = y - x + 9 * np.cos(t)
dx = -10*np.sin(t) + np.cos(t)
dy = np.cos(t) - np.sin(t)

dl = np.sqrt(dx**2 + dy**2)
L = (dl*dt).sum()

y_ = lambda x,t:x-9*np.cos(t)