integral_demo.py

from pylab import *
from matplotlib.patches import Polygon

def func(x):
    return (x-3)*(x-5)*(x-7)+85

def integral_plot(f):
    ax = subplot(111)
    a, b = 2, 9 # integral area
    x = arange(0, 10, 0.01)
    y = f(x)
    plot(x, y, linewidth=1)
    # make the shaded region
    ix = arange(a, b, 0.01)
    iy = func(ix)
    verts = [(a,0)] + list(zip(ix,iy)) + [(b,0)]
    poly = Polygon(verts, facecolor='0.8', edgecolor='k')
    ax.add_patch(poly)

    text(0.5 * (a + b), 30,
         r"$\int_a^b f(x)\mathrm{d}x$", horizontalalignment='center',
         fontsize=20)

    axis([0,10, 0, 180])
    figtext(0.9, 0.05, 'x')
    figtext(0.1, 0.9, 'y')
    ax.set_xticks((a,b))
    ax.set_xticklabels((r'$a$',r'$b$'))
    ax.set_yticks([])
    show ()