approx_integral.py

def approximate_integral(self, x0, x1):
    """
        Estimates the definite integral of the function using the Taylor series expansion.

        x0 - lower limit of integration
        x1 - upper limit of integration 
    """

    # integrals can be off by a constant since int(f(x)) = F(x) + C
    value = 0
    for i in range(len(self.coefficients)):
        value += ((self.coefficients[i] * (1/(i+1)) * ((x1 - self.center)**(i+1))) - 
                  (self.coefficients[i] * (1/(i+1)) * ((x0 - self.center)**(i+1)))) # integrate each term: x^n => (1/n+1)*x^(n+1)
    return value