Cubic Integral

cubic_integral(first_constant, second_constant, third_constant, fourth_constant, precision=4)

Generates the integral of a cubic function

Parameters

• first_constant (int or float) – Coefficient of the cubic term of the original cubic function; if zero, it will be converted to a small, non-zero decimal value (e.g., 0.0001)

• second_constant (int or float) – Coefficient of the quadratic term of the original cubic function; if zero, it will be converted to a small, non-zero decimal value (e.g., 0.0001)

• third_constant (int or float) – Coefficient of the linear term of the original cubic function; if zero, it will be converted to a small, non-zero decimal value (e.g., 0.0001)

• fourth_constant (int or float) – Coefficient of the constant term of the original cubic function; if zero, it will be converted to a small, non-zero decimal value (e.g., 0.0001)

• precision (int, default=4) – Maximum number of digits that can appear after the decimal place of the resultant roots

Raises

• TypeError – First four arguments must be integers or floats

• ValueError – Last argument must be a positive integer

Returns

• integral[‘constants’] (list of float) – Coefficients of the resultant integral

• integral[‘evaluation’] (func) – Function for evaluating the resultant integral at any float or integer argument

See also

cubic_equation(), cubic_derivatives(), cubic_roots(), cubic_model()

Notes

• Standard form of a cubic function: \(f(x) = a\cdot{x^3} + b\cdot{x^2} + c\cdot{x} + d\)

• Integral of a cubic function: \(F(x) = \frac{a}{4}\cdot{x^4} + \frac{b}{3}\cdot{x^3} + \frac{c}{2}\cdot{x^2} + d\cdot{x}\)

• Basic Properties of Indefinite Integrals

• Basic Integration Forumulas

Examples

Import cubic_integral function from regressions library

>>> from regressions.analyses.integrals.cubic import cubic_integral

Generate the integral of a cubic function with coefficients 2, 3, 5, and 7, then display its coefficients

>>> integral_constants = cubic_integral(2, 3, 5, 7)
>>> print(integral_constants['constants'])
[0.5, 1.0, 2.5, 7.0]

Generate the integral of a cubic function with coefficients 7, -5, -3, and 2, then evaluate its integral at 10

>>> integral_evaluation = cubic_integral(7, -5, -3, 2)
>>> print(integral_evaluation['evaluation'](10))
15703.3

Generate the integral of a cubic function with all inputs set to 0, then display its coefficients

>>> integral_zeroes = cubic_integral(0, 0, 0, 0)
>>> print(integral_zeroes['constants'])
[0.0001, 0.0001, 0.0001, 0.0001]