Part2
from math import *
from simpson import *
k=1
def f(x): return (exp(-(x**2)))
E = error(f,-2.0,2.0,k)
while(E > 1e-4):
k += 1
E = error(f,-2.0,2.0,k)
I = simpson(f,-2.0,2.0,k)
print "Integral from [-2.0,2.0] of e^(-x^2) = ",I
print "Error: ", E
print "Minimal Intervals for 10^-4 = ",2**k
print ""
k=1
def f(x): return 8*(sqrt(1+cos(2*x)))
E = error(f,0.0,4.0,k)
while(E > 1e-4):
k += 1
E = error(f,0.0,4.0,k)
I = simpson(f,0.0,4.0,k)
print "Integral from [0.0,4.0] of 8*(sqrt(1+cos(2*x))) = ",I
print "Error: ", E
print "Minimal Intervals for 10^-4 = ", 2**k
print ""
k=1
def f(x): return (100.0/(x**2))
E = error(f,1.0,3.0,k)
while(E > 1e-4):
k += 1
E = error(f,1.0,3.0,k)
I = simpson(f,1.0,3.0,k)
print "Integral from [1,3] of 100/x^2 = ",I
print "Error: ", E
print "Minimal Intervals for 10^-4 = ",2**k
print ""
k=8
def f(x): return (exp(-(x**2)))
E = error(f,-2.0,2.0,k)
while(E > 1e-8):
k += 1
E = error(f,-2.0,2.0,k)
I = simpson(f,-2.0,2.0,k)
print "Integral from [-2.0,2.0] of e^(-x^2) = ",I
print "Error: ", E
print "Minimal Intervals for 10^-8 = ",2**k
print ""
k=8
def f(x): return 8*(sqrt(1+cos(2*x)))
E = error(f,0.0,4.0,k)
while(E > 1e-8):
k += 1
E = error(f,0.0,4.0,k)
I = simpson(f,0.0,4.0,k)
print "Integral from [0.0,4.0] of 8*(sqrt(1+cos(2*x))) = ",I
print "Error: ", E
print "Minimal Intervals for 10^-8 = ",2**k
print ""
k=8
def f(x): return (100.0/(x**2))
E = error(f,1.0,3.0,k)
while(E > 1e-8):
k += 1
E = error(f,1.0,3.0,k)
I = simpson(f,1.0,3.0,k)
print "Integral from [1,3] of 100/x^2 = ",I
print "Error: ", E
print "Minimal Intervals for 10^-8 = ",2**k
print ""
![Part2
frommathimport *
fromsimpsonimport *
k=1
deff(x):return(exp(-(x**2)))
E= error(f,-2.0,2.0,k)
while(E> 1e-4):
k += 1
E= error(f,-2.0,2.0,k)
I = simpson(f,-2.0,2.0,k)
print "Integralfrom[-2.0,2.0] ofe^(-x^2) = ",I
print "Error:", E
print "MinimalIntervals for 10^-4 = ",2**k
print ""
k=1
deff(x):return8*(sqrt(1+cos(2*x)))
E= error(f,0.0,4.0,k)
while(E> 1e-4):
k += 1
E= error(f,0.0,4.0,k)
I = simpson(f,0.0,4.0,k)
print "Integralfrom[0.0,4.0] of8*(sqrt(1+cos(2*x))) = ",I
print "Error:", E
print "MinimalIntervals for 10^-4 = ", 2**k
print ""
k=1
deff(x):return(100.0/(x**2))
E= error(f,1.0,3.0,k)
while(E> 1e-4):
k += 1
E= error(f,1.0,3.0,k)
I = simpson(f,1.0,3.0,k)
print "Integralfrom[1,3] of100/x^2 = ",I
print "Error:", E
print "MinimalIntervals for 10^-4 = ",2**k
print ""
k=8
deff(x):return(exp(-(x**2)))
E= error(f,-2.0,2.0,k)
while(E> 1e-8):
k += 1
E= error(f,-2.0,2.0,k)
I = simpson(f,-2.0,2.0,k)
print "Integralfrom[-2.0,2.0] ofe^(-x^2) = ",I
print "Error:", E
print "MinimalIntervals for 10^-8 = ",2**k
print ""
k=8
deff(x):return8*(sqrt(1+cos(2*x)))
E= error(f,0.0,4.0,k)
while(E> 1e-8):
k += 1
E= error(f,0.0,4.0,k)
I = simpson(f,0.0,4.0,k)
print "Integralfrom[0.0,4.0] of8*(sqrt(1+cos(2*x))) = ",I
print "Error:", E
print "MinimalIntervals for 10^-8 = ",2**k
print ""](https://image.slidesharecdn.com/2245-180713125016/85/Part2-from-math-import-from-simpson-import-k-1-def-f-x-return-exp-x-2-E-error-f-2-0-1-320.jpg)
![k=8
deff(x):return(100.0/(x**2))
E= error(f,1.0,3.0,k)
while(E> 1e-8):
k += 1
E= error(f,1.0,3.0,k)
I = simpson(f,1.0,3.0,k)
print "Integralfrom[1,3] of100/x^2 = ",I
print "Error:", E
print "MinimalIntervals for 10^-8 = ",2**k
print ""](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)