Examine two ways a line changes:
. What are ? How are the function values changing as increases?
Compute the finite differences (that is, find the difference in
-values as increases) and look for a pattern.
Calculate the area under the curve for
if . How is the area changing as increases?
Use geometry to find the area of the trapezoid between
and for each value of . Keep your results organized.
Is the difference between the areas growing constantly or linearly? If not, how else could it be growing, and by what pattern each time?