How do I plot the integral of e^(-t^2) from x=0 to x=3 in Python?

Question

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?

Answer 1

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!