An accumulation function, also known as an antiderivative or indefinite integral, represents the reverse process of differentiation. It calculates the original function when its derivative is given.
A definite integral calculates the accumulated area under a curve between two specified limits. It represents the total change or accumulation within a specific interval.
The fundamental theorem of calculus establishes a connection between differentiation and integration. It states that if F(x) is an antiderivative (accumulation function) of f(x), then ∫[a,b] f(x) dx = F(b) - F(a).
An initial condition refers to specifying a particular value for a variable at an initial point in time or space. In terms of accumulation functions, it helps determine the constant term added during integration to account for unknown values.