The Linear Accumulation Function, usually denoted as ( F(x) ), is a continuous function that represents the accumulation of a constant rate over an interval.

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It’s given by the formula:

[ F(x) = \int_{a}^{x} f(t) \, dt ]

For a constant function ( f(t) = c ), where ( c ) is a real number, the integral becomes:

[ F(x) = \int_{a}^{x} c \, dt ]

Integrating a constant yields ( c \cdot (x – a) ), and for any real numbers ( a ) and ( x ), this expression is valid. Thus, the Linear Accumulation Function is valid for all real numbers when ( f(t) ) is a constant function.