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Solution Review: Integrating Complex Functions

Understand how to use SymPy to compute and integrate Taylor series with customizable integration limits in Python. This lesson guides you through setting default parameters, evaluating integrals to significant figures, and applying flexible function arguments to perform symbolic integration of complex functions.

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Solution #

C++
from sympy import *
def f(x):     # just a mathematical function
  return atan(x)
def g(x):       # just a mathematical function
  return exp(x)
x = Symbol('x')
def ts_integral(f, x, n=4, lim1=None, lim2=None):
  ts = f(x).series(x, 0, n).removeO()
  integral = integrate(ts, (x, lim1, lim2))
  return ts, integral.evalf(3) 
output_1 = ts_integral(f, x, 10, 0, pi/4)
output_2 = ts_integral(g, x)
print("Taylor Series of f(x):", output_1[0])
print("Integral of f(x):", output_1[1])
print("-----")
print("Taylor Series of g(x):", output_2[0])
print("Integral of g(x):", output_2[1])

Explanation #

  • In the ...