f="-x**2"
a=1
b=5
n=8
def lSum(f,a,b,n):
h=(b-a)/n
l=sum([f(a+i*h)*h for i in range(n)])
return l
def rSum(f,a,b,n):
h=(b-a)/n
l=sum([f(a+i*h)*h for i in range(n)])
return l-f(a)*h+f(b)*h
def tSum(f,a,b,n):
h=(b-a)/n
l=sum([f(a+i*h)*h for i in range(n)])
r=l-f(a)*h+f(b)*h
return (r+l)/2
def tError(f,a,b,n):
h=(b-a)/n
l=sum([f(a+i*h)*h for i in range(n)])
r=l-f(a)*h+f(b)*h
return (r-l)/2
l=lSum(lambda x: eval(f),a,b,n).n(digits=6)
r=rSum(lambda x: eval(f),a,b,n).n(digits=6)
t=tSum(lambda x: eval(f),a,b,n).n(digits=6)
e=tError(lambda x: eval(f),a,b,n).n(digits=6)
print "l\t\tr\t\tt\t\te"
print l,"\t",r,"\t",t,"\t",e
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l r t e
-35.5000 -47.5000 -41.5000 -6.00000
l r t e
-35.5000 -47.5000 -41.5000 -6.00000
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