Integrals In Python: Add Object Not Callable

I'm trying to solve an integral of a taylor approximation of a sin(x) function by using the trapezoid rule. The code seems fine but it keep giving me the following error: 'TypeErro

Solution 1:

In your case f is a sympy expression. You cannot just evaluate it by calling it; you have to use the evalf() method:

...
integral += 0.5*(xedge[n+1] - xedge[n])*(f.evalf(xedge[n]) + f.evalf(xedge[n+1]))
...

Produces the output:

Taylor series:x**5/120-x**3/6+xTrapezoid rule result:0.0079345703125*x**5-0.158203125*x**3+1.0*xEnd

Solution 2:

Your command f = sin(x) is invalid; the argument is a sympy.Symbol, not a legal argument to the sin function.

For future reference, here's how I broke down the problem to isolate the error. Replacing f with sin worked around the problem ... likely not what you need for your assignment, but useful in debugging.

import math
import numpy
import sympy as sy
import numpy as np
from sympy.functions import sin,cos
import matplotlib.pyplot as plt
x = sy.Symbol('x')
print"sy.Symbol('x') is", x, type(x)
f = sin(x)

# Factorial function that will be used in the Taylor approximationdeffactorial(n):
    if n <= 0:
        return1else:
        return n*factorial(n-1)

taylor_series = sin(x).series(n=None)

#def fun(x):#   return numpy.sin(x)# Do a trapezoid integration by breaking up the domain [a,b] into N slabsdeftrap(a,b,f,N):

    xedge = numpy.linspace(a,b,N+1)

    integral = 0.0

    n = 0while n < N:
        x0 = xedge[n]
        x1 = xedge[n+1]
        print x0, x1
        sub1 = x1 - x0
        f0 = math.sin(x0)
        f1 = math.sin(x1)
        sub2 = f0 + f1
        integral = integral + 0.5 * sub1 * sub2
        n += 1return integral


N = 3
a = 0.0
b = 1.0# takes the number of terms desired for your generator
z = sum([next(taylor_series) for i inrange(N)])
print("Taylor series:",z)

# Trapezoid rule result and calculaiton of error term
N = 2while (N <= 2):
    dd = trap(a,b,z,N)
    print ('Trapezoid rule result:', dd)
    N *= 2