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"""Module for integrating functions by the Midpoint rule."""
from math import *
import sys
def integrate(f, a, b, n):
"""Return the integral of f from a to b with n intervals."""
h = float(b-a)/n
s = 0
for i in range(1, n+1):
s += f(a + (i-0.5)*h)
return s*h
def test_integrate():
"""Check that linear functions are integrated exactly."""
def g(x):
return p*x + q # general linear function
def int_g_exact(x): # integral of g(x)
return 0.5*p*x**2 + q*x
a = -1.2; b = 2.8 # "arbitrary" integration limits
p = -2; q = 10
success = True # True if all tests below are passed
for n in 1, 10, 100:
I = integrate(g, a, b, n)
I_exact = int_g_exact(b) - int_g_exact(a)
error = abs(I_exact - I)
if error > 1E-14:
success = False
assert success
def main():
Read f-formula, a, b, n from the command line.
Print the result of integrate(f, a, b, n).
f_formula = sys.argv[1]
a = eval(sys.argv[2])
b = eval(sys.argv[3])
n = int(sys.argv[4])
except IndexError:
print 'Usage: %s f-formula a b n' % sys.argv[0]
from scitools.std import StringFunction
f = StringFunction(f_formula)
I = integrate(f, a, b, n)
print I
if __name__ == '__main__':
if sys.argv[1] == 'verify':
# Compute the integral specified on the command line