What lies beneath the accumulation function?

Accumulation

If the integrand ƒ is a continuous function, then the corresponding

accumulation function, , has the same domain as ƒ. When

A(x) makes sense even if x is to the left of a, we can use the sign convention:

The Sign Convention

Sketch the graph ƒ(t) = t and complete the table of values for the function A(x).

x 0 1 2 3 4

x 0 -1 -2 -3 -4

On the graphing calculuator ...

The Second Fundamental Theorem of Calculus

If ƒ is a continuous function on some interval [a, b] and an accumulation

function A is defined by then

Let's look at this geometrically ...

Given each accumulation function A(x), find it's derivative A'(x).