Tukukkk

I need to both calculate and plot the integral below in Python:

integral of the function e^(-t^2) from x=0 to x=3

So far I've managed to calculate the integral using Simpson's rule. The next bit which I'm struggling with is plotting the integral of e^(-t^2) vs x from x=0 to x=3 (see the image above).

Here's the code I've written to calculate the integral -

from math import exp



def f(t):

    return exp(-(t**2))



a = 0

b = 3

h = 0.1

N = int((b-a)/h)

s_even = 0

s_odd = 0



for k in range(1,N,2):

    s_odd += f(a+k*h)



for k in range(2,N,2):

    s_even += f(a+k*h)



s = f(a) + f(b) + 4*s_odd + 2*s_even

Integral = h*s/3

print(Integral)

How do I then create a graph of this integral?

Here's a script I wrote that performs your calculation and plots it using PyQtGraph:

from pyqtgraph.Qt import QtGui, QtCore

import pyqtgraph as pg



from math import exp



class I:



    def f(self,t):

        return exp(-(t**2))



    def __init__(self, a = 0, b = 3, h = 0.1):

        N = int((b-a)/h)

        s_even = s_odd = 0

        for k in range(1,N,2):

            s_odd += self.f(a+k*h)



        for k in range(2,N,2):

            s_even += self.f(a+k*h)



        s = self.f(a) + self.f(b) + 4*s_odd + 2*s_even

        self.I = h*s/3



    def __str__(self):

        return "I: %s" % self.I



def plot(array):

    app = QtGui.QApplication()

    win = pg.GraphicsWindow(title="Basic plotting examples")

    win.resize(1000,600)

    win.setWindowTitle('pyqtgraph example: Plotting')



    # Enable antialiasing for prettier plots

    pg.setConfigOptions(antialias=True)



    p1 = win.addPlot(title="Basic array plotting", y=array)



    QtGui.QApplication.instance().exec_()



def main():

    a=0

    b=a+0.001

    points=

    while(a<3):

        points.append(I(a,b).I)

        a=b

        b=a+0.001

    plot(points)





## Start Qt event loop unless running in interactive mode or using pyside.

if __name__ == '__main__':

    main()

Here is the graph it draws:

Thanks for your help Red Cricket. It looks like you may have graphed the function e^(-t^2) rather than the integral of that function. Nonetheless, I think I've worked it out; I've discovered scipy has an integrate function:

from math import exp

from numpy import arange

from scipy import integrate



def f(t):

    return exp(-(t**2))



a = 0

b = 3

h = 0.1

N = int((b-a)/h)



s_even = 0

s_odd = 0



for k in range(1,N,2):

    s_odd += f(a+k*h)



for k in range(2,N,2):

    s_even += f(a+k*h)



s = f(a) + f(b) + 4*s_odd + 2*s_even

I = h*s/3



function = 

x = 

for t in arange(0,4,h):

    function.append(f(t))

for i in arange(0,4,h):

    x.append(i)



function_int = integrate.cumtrapz(function,x,initial=0)



plot(x,function_int)

show()

print(I)

This produces a graph of the integral and prints the final value of the integral itself. Hooray!