Python中的梯形和辛普森规则? [英] Trapezoid and Simpson rule in Python?

问题描述

我必须在python中为函数e^((-x)^2)编写梯形和辛普森规则.

I have to write the trapezoid and simpson rule in python for the function e^((-x)^2).

这是我到目前为止所得到的.它给出的答案是8218.7167913，但是根据我的老师的回答是类似1.77251356....的东西.

Here's what I got so far. The answer it gives out is 8218.7167913 but the answer according to my teacher is something like 1.77251356.....

我哪里出错了?

from numpy import *

def f(x):
    return e**((-x)**2)

def trapezoid(f, a, b, n):
    deltax = float(b - a)/(n)
    h = float(b - a) / n
    s = 0.0
    s += f(a)/2.0
    for i in range(1, n):
        s += f(a + i*h)
    s += f(b)/2.0
    return s * h

print trapezoid(f, -3, 3, 6)

推荐答案

查看您的函数:e^((-x)^2).负号没有做任何事情，因为您要立即将其除掉.好像很奇怪您更有可能应该集成e^(-x^2).让我们测试一下:

Look at your function: e^((-x)^2). The negative sign isn't doing anything because you're squaring it away immediately. That seems strange. More likely is that you were supposed to integrate e^(-x^2). Let's test:

>>> trapezoid(lambda x: e**((-x)**2), -3, 3, 1000)
2889.3819494560144
>>> trapezoid(lambda x: e**(-x**2), -3, 3, 1000)
1.7724146920763713

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