File:Riemann Integration and Darboux Lower Sums.gif

# Author: Ika, 2013-09-14

import numpy as np
import matplotlib.pyplot as plt
import scipy.special as sp
from matplotlib.patches import Polygon
import random                                                                        

fig=plt.figure()
ax = fig.add_subplot(111)

ax.set_xlim(0,2)
ax.set_ylim(0,4)

X = np.arange(0,2.01,0.01)
Y = X*X

ax.plot(X, Y)

verts = [(0,0)] + zip(X,Y) + [(2,0)]
poly = Polygon(verts, facecolor='blue',alpha=0.5,edgecolor='blue')
ax.add_patch(poly)
plt.savefig("frame0100.jpg")

ord = 0;
while (ord<7):
	plt.clf()
	fig=plt.figure()
	ax = fig.add_subplot(111)
	interval = 1.0/(2**ord)
	ax.set_xlim(0,2)
	ax.set_ylim(0,4)

	X = np.arange(0,2.01,0.01)
	Y = X*X

	ax.plot(X, Y)
	ax.text(0.2,3.0,'Step=1/'+str(2**ord),size=36);
	x=interval;
	while (x<2+interval/2.0):
		verts = [(x-interval,0)]+[(x-interval,(x-interval)*(x-interval))]+[(x,(x-interval)*(x-interval))]+[(x,0)];
		poly = Polygon(verts, facecolor='blue', alpha=0.5,edgecolor='black')
		ax.add_patch(poly)
		x=x+interval;

	plt.savefig("frame00"+str(ord)+".jpg");
	
	ord = ord+1;