python集成问题，函数具有指数

Question

I would like to integrate the function e^(-x**2/2) by simpson rule but it is keep having an error and I don't know what is the problem.

a=eval(input('a:'))
b=eval(input('b:'))
n=eval(input('n:'))
def f(x):
    e**(-x**2/2)
h=(b-a)/n
s= f(a)+f(b)
def simpson_rule(f(x),a,b,n):

  #Approximation by Simpson's rule
  c=(a+b)/2.0
  h=abs(b-a)/2.0
  return h*(f(a)+4.0*f(c)+f(b))/3.0
def simpson_rule(f(x),a,b,n):
    """Approximates the definite integral of f from a to b by the composite Simpson's rule, using n subintervals"""
    for i in range (1,n,2):
        s+=4*f(a+i*h)
    for i in range(2,n-1,2):
        s+=2*f(a+i*h)
    return s*h/3
print simpson_rule(f(x),a,b,n)

Answer 1

You define 2 integration routines with the same name. Which one do you expect to run if you call simpson_rule() ? The first one is the special case where n=1. You might rename it accordingly.

Second, your call is print simpson_rule(f(x),a,b,n) but you only need to hand over f() to the function, like this print simpson_rule(f,a,b,n) . You can see that f is a function, and f() is a function return value:

 def f(x): return x + 13 f <function f at 0x0000000002253D68> f(5) 18 

Try it out and if you still have errors please post the error message(s).