import numpy as np
import matplotlib.pyplot as plt

def fun_f(x):
    return np.cos(x)

def fun_abs_f(x):
    return abs(np.cos(x))

x_a = np.pi/2
x_b = 2*np.pi
dx = 0.01
N = int((x_b - x_a)/dx + 1)
x_array = np.linspace(x_a, x_b, N)
k_array = np.arange(0, N)

plt.close('all')
plt.plot(x_array, fun_f(x_array), label='f(x)')
plt.plot(x_array, np.zeros(len(x_array)), label='x-axis')
plt.legend()
plt.grid()
plt.xlabel('x')

# plt.savefig('plott_areal.pdf')
plt.show()

f_array = fun_f(x_array)
Integral = (np.sum((f_array[0:-1] + f_array[1:]))/2)*dx

f_abs_array = fun_abs_f(x_array)
Areal=(np.sum((f_abs_array[0:-1]+f_abs_array[1:]))/2)*dx

print('Integral = ', Integral)
print('Areal  = ', Areal)