Integration
Just as differentiation gives a quantity's rate of change in an instant, integration gives the accumulation of a quantity
over an interval. Whereas the derivative solved the instantaneous rate of change (or, slope) problem, integration solves
the accumulation (or, area) problem. These are related by the Fundamental Theorem of Calculus Part 1 (FTOCP1):
$\frac{d}{dx} \int_{a}^{x} f(t)dt = f(x)$
Exercises
14. Suppose y = f(t) is graphed below. Complete the provided table of values, to two decimal places, for the area
accumulation function $A(x) = \int_{-2}^{x} f(t)dt$.
15. Determine A'(4), or explain why it does not exist.
16. Determine A''(4), or explain why it does not exist.
Discussion
17. Interpret the FTOCP1, graphically, using one or two complete sentences.
