Quadratic Integral

quadratic_integral(first_constant, second_constant, third_constant, precision=4)

Generates the integral of a quadratic function

Parameters

• first_constant (int or float) – Coefficient of the quadratic term of the original quadratic 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 linear term of the original quadratic 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 constant term of the original quadratic 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 three 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

quadratic_equation(), quadratic_derivatives(), quadratic_roots(), quadratic_model()

Notes

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

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

• Basic Properties of Indefinite Integrals

• Basic Integration Forumulas

Examples

Import quadratic_integral function from regressions library

>>> from regressions.analyses.integrals.quadratic import quadratic_integral

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

>>> integral_constants = quadratic_integral(2, 3, 5)
>>> print(integral_constants['constants'])
[0.6667, 1.5, 5.0]

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

>>> integral_evaluation = quadratic_integral(7, -5, 3)
>>> print(integral_evaluation['evaluation'](10))
2113.3

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

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