accumulation function

A function built by running a "total so far" tally of another function's area underneath it.

Given a function $f$ , its accumulation function is $A(x) = \int_a^x f(t)\,dt$ for a fixed starting point $a$ : the signed area under $f$ from $a$ up to the variable endpoint $x$ . As $x$ moves, $A(x)$ tracks the running total of that area, and the first part of the Fundamental Theorem of Calculus says $A'(x)=f(x)$ .

Examples

If $f(t)=t$ , then $A(x)=\int_0^x t\,dt=\dfrac{x^2}{2}$ accumulates the triangular area under the line $y=t$ from $0$ to $x$ .