prTrap

from numpy import *
from pylab import *

def f(x):
    return -(x**4/12.)+(5*x**2/2.)
def d2f(x):
    return 5-x**2

a=0.
b=2.
eps=10**(-4)

xt=linspace(a,b,10)
plot(xt,d2f(xt),0.,d2f(0),'co')
show()
M2=d2f(1)
n=ceil((b-a)*sqrt((M2*(b-a))/12./eps))
print ('Broj podsegmenata:'),n
h=(b-a)/n
x=linspace(a,b,n+1)
y=f(x)
t=trapz(y,x)
pt=h/2.*(y[0]+2*sum(y[1:n])*y[n])
print ('Vrijednost integrala primjenom trapezne formule:'),t
print ('Vrijednost integrala primjenom produljene trapezne formule:'),pt
print ('Apsolutna greska produljene trapezne formule:'),(b-a)/12.*h**2*M2