The document discusses the accumulation function and its properties. It introduces the accumulation function, defines its domain as the same as the integrand, and establishes a sign convention for when the accumulation function is defined for values less than the lower bound. It also references the second fundamental theorem of calculus relating the accumulation function to its derivative and poses exercises to find accumulation functions and their derivatives given integrands.

1. What lies
beneath the
accumulation
function?
Accumulation

2. The Sign Convention
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:

3. 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

4. On the graphing calculuator ...

5. 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 ...

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