Accumulation of Function

accumulated_area(equation_type, coefficients, start, end, precision=4)

Evaluates the definite integral between two points for a specific function

Parameters

• equation_type (str) – Name of the type of function for which the definite integral must be evaluated (e.g., ‘linear’, ‘quadratic’)

• coefficients (list of int or float) – Coefficients of the original function to integrate

• start (int or float) – Value of the x-coordinate of the first point to use for evaluating the definite integral

• end (int or float) – Value of the x-coordinate of the second point to use for evaluating the definite integral

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

Raises

• ValueError – First argument must be either ‘linear’, ‘quadratic’, ‘cubic’, ‘hyperbolic’, ‘exponential’, ‘logarithmic’, ‘logistic’, or ‘sinusoidal’

• TypeError – Second argument must be a 1-dimensional list containing elements that are integers or floats

• TypeError – Third and fourth arguments must be integers or floats

• ValueError – Third argument must be less than or equal to fourth argument

• ValueError – Last argument must be a positive integer

Returns

area – Definite integral of the original equation, evaluated between two points; if start and end values are identical, then definite integral will be zero

Return type

float

See also

linear_integral(), quadratic_integral(), cubic_integral(), hyperbolic_integral(), exponential_integral(), logarithmic_integral(), logistic_integral(), sinusoidal_integral()

Notes

• Definite integral of a function: \(\int_{a}^{b} f(x) \,dx = F(b) - F(a)\)

• Definite Integral

• Fundamental Theorem of Calculus

Examples

Import accumulated_area function from regressions library

>>> from regressions.analyses.accumulation import accumulated_area

Evaluate the definite integral of a linear function with coefficients 2 and 3 between the end points 10 and 20

>>> area_linear = accumulated_area('linear', [2, 3], 10, 20)
>>> print(area_linear)
330.0

Evaluate the definite integral of a cubic function with coefficients 8, 6, -10, and 7 between the end points 10 and 20

>>> area_cubic = accumulated_area('cubic', [8, 6, -10, 7], 10, 20)
>>> print(area_cubic)
312570.0