Question

I know how to integrate a function with Scipy. I do it in this way:

    from scipy import *
    from scipy import integrate
    integral = integrate.simps(y,x)

In this way I integrate with the Simpsons’ rule the function y(x), but what if I want to integrate this function in cylindrical coordinates?
I mean, instead of the integral \int y(x)dx I want to solve the integral \int y(x)*2*pi*x*dx.

I tried with

    integral = integrate.simps(y,x**2.*pi)

But it doesn’t seem to return the correct result.

I am integrating data points, not functions!

Answer 1

You should try

integral = integrate.simps(y*x*2*pi,x)

where y should be an array of function values at the positions x. Note that 2*pi*x is the necessary factor to add to your integrand (as you pointed out yourself).