So I was doing calculus homework tonight. Numerical estimation of integrals, using left endpoint, right endpoint, midpoint and trapezoidal estimation. I thought that it was really tedious to write all that out by hand, so I thought I'd have the computer do it for me. Voila. A python script that will numerically estimate integrals. Although you could just go to Wolfram Alpha.
Edit: added simpson's rule
69 lines of beauty:
#Numerical estimation of integrals
from math import *
def main():
f = lambda x: x**3
print left(f)
print right(f)
print midpoint(f)
print trapezoid(f)
f = lambda x: abs(8-x)
print midpoint(f, 4, 7.0, 13.0)
print trapezoid(f, 4, 7.0, 13.0)
print simpson(f, 4, 7.0, 13.0)
f = lambda x: e**(-5*x**2)
print trapezoid(f, 4, 0.0, 1.0)
print midpoint(f, 4, 0.0, 1.0)
print simpson(f, 4, 0.0, 1.0)
def left(function, n = 20, start = 0.0, end = 10.0):
s = 0
dist = end-start
deltaX = dist/n
for x in range(n):
s += function(start + deltaX*x)
return s*deltaX
def right(function, n = 20, start = 0.0, end = 10.0):
s = 0
dist = end-start
deltaX = dist/n
for x in range(n):
s += function(start + deltaX*(x+1))
return s*deltaX
def midpoint(function, n = 20, start = 0.0, end = 10.0):
s = 0
dist = end-start
deltaX = dist/n
for x in range(n):
s += function(start + 1/2.0*(deltaX*x+deltaX*(x+1)))
return s*deltaX
def trapezoid(function, n = 20, start = 0.0, end = 10.0):
s = 0
dist = end-start
deltaX = dist/n
for x in range(n+1):
if x in (0, n):
s += function(start + deltaX*(x))
else:
s += 2*function(start + deltaX*(x))
return s*deltaX/2
def simpson(function, n = 20, start = 0.0, end = 10.0):
s = 0
dist = end-start
deltaX = dist/n
for x in range(n+1):
if x in (0, n):
s += function(start + deltaX*x)
elif x%2 == 1:
s += 4*function(start + deltaX*x)
else:
s += 2*function(start + deltaX*x)
return s*deltaX/3
if __name__ == "__main__":
main()
