How to explain the difference between the FFT result and the analytical Fourier transform?

Question

I am learning FFT by scipy's 'fft'. And now I have the rectangle function as shown below.

Its analytical Fourier transform is

and its squared absolute value is

For performing FFT, I sampled the f(x) in the range 0 <= x <= 10. And the number of samples N is 2**18, such that sample interval delt is 10.0/(2**18-1). The FFT snippet is shown below.

import numpy as np
from scipy.fft import fft, ifft

# Define the analytical form of the Fourier transform
def fk(k):
    value = 2*(1-np.cos(k))/(k**2 + 0.0001)   # '0.0001' is used to aovid the singularity
    return value


N = 2**18
delt = 10.0/(N-1)                              # sample interval
y_time = np.loadtxt("data_input_b_262144.dat") # read-in the sample points
y_freq = fft(y_time)                           # perform fft
y_freq_square =(delt**2)* np.abs(y_freq)**2   # The squared absolute value of magnitude of frequencce component

# Positive frequency
k = np.linspace(0.0, 1.0/(2.0*delt), int(N/2))

# Plot the spectrum
plt.plot(k, y_freq_square[0:int(N/2)],
         k,fk(k))
plt.gca().set_xlim(0.1, np.amax(k))
plt.gca().set_ylim(0.001, 1.2)
plt.gca().set_xscale('log')
plt.gca().set_yscale('log')
plt.xlabel('k')
plt.ylabel('$\hat f(k)$')
plt.legend(['fft result', 'analytical fourier transform'])
plt.savefig('rectangle_fft.png')

The figure is

So my question is that why does there exist differences between these two results? In principle, they are supposed to be the same curve in the figure.