Question

I would like to write a program that solves the definite integral below in a loop which considers a different value of the constant c per iteration.

I would then like each solution to the integral to be outputted into a new array.

How do I best write this program in python?

with limits between 0 and 1.

from scipy import integrate

integrate.quad

Is acceptable here. My major struggle is structuring the program.

Here is an old attempt (that failed)

# import c
fn = 'cooltemp.dat'
c = loadtxt(fn,unpack=True,usecols=[1])

I=[]
for n in range(len(c)):

    # equation
    eqn = 2*x*c[n]

    # integrate 
    result,error = integrate.quad(lambda x: eqn,0,1)

    I.append(result)

I = array(I)

Answer 1

You’re really close.

fn = 'cooltemp.dat'
c_values = loadtxt(fn,unpack=True,usecols=[1])

I=[]
for c in c_values: #can iterate over numpy arrays directly.  No need for `range(len(...))`

    # equation
    #eqn = 2*x*c[n] #This doesn't work, x not defined yet.

    # integrate 
    result,error = integrate.quad(lambda x: 2*c*x, 0, 1)

    I.append(result)

I = array(I)

I think you’re a little confused about how lambda works.

my_func = lambda x: 2*x

is the same thing as:

def my_func(x):
    return 2*x

If you still don’t like lambda, you can do this:

f(x,c):
   return 2*x*c

#...snip...
integral, error = integrate.quad(f, 0, 1, args=(c,) )