Pfthb

I'm having difficulties creating a simple for loop code to integrate a given function without using SymPy. I'm thinking using some sort of Riemann approximation but I don't know how to do this exactly. The code I have so far is:

def xsquared(x):
 n = 2
 return x**n

def integral(fun, xmin, xmax):
 total = 0
 for a in range(xmin, xmax):
 x = a
 total += fun(x*1.235)
 return total 

print(integral(xsquared, 0, 4))

The output gives 21.3 but how do I do this without inputting a number referring to the "fun(x*1.235)" part?

Any help would be appreciated.

To compute integral by Riemann means that you are computing the limit of Riemann's sum by making partitions innner (Wikipedia).

For that, your function could have a new parameter interval: dx or maybe you could just guess the interval by splitting the full range into N equal sized intervals. Here is an example asking dx as argument.

Then, your function should be:

def riemann(fun, xmin, xmax, dx):
 total = 0
 a = xmin
 while a < xmax:
 total += fun(a + dx/2)*dx
 a += dx
 return total

Example Outputs

print(riemann(xsquared, 0, 4, 0.1))
> 21.330000000000013

print(riemann(xsquared, 0, 4, 0.25))
> 21.3125

print(riemann(xsquared, 0, 4, 0.5))
> 21.25

Analythic resolution gives: 64/3 ~ 21.33333

You're aproximating then the integral by computing the area of the rectangle having:

• 
  height: the function value at interval middle point fun(a + dx/2)
  


• 
  width: the interval length (dx)

Note: if xmax < xmin, you should verify that dx < 0.