Riemann Sum (Midpoint)

riemann_midpoint.py

def rsm(f, x0, xn, n):
    """Approximates integral using Riemann sum of the midpoint.
       Takes the function f(x), bounds a and b, and number of partitions, n as arguments."""
    dx = (xn - x0) / n
    return [f(x0 + i*dx) for i in range(0,n)]

x0 = 0
xn = 2
n = 4
dx = (xn - x0) / n
xs = np.linspace(x0, xn, 100)
fig = plt.figure()
ax = fig.add_axes([0.1,0.1,0.8,0.8])
ax.plot(xs, [x**3 for x in xs])
for i in range(0, n):
    x = x0 + i*dx + dx/2
    ax.scatter(x, x**3, color='r')
    ax.add_patch(Rectangle((x-dx/2, 0), dx, x**3))