The idea that the definite integral is an “accumulator” means that integrating a rate of change over an integral gives the net amount of change over the interval.Many of the application of integration are based on this idea. Here are some past posts on this idea.
Accumulation An introductory activity to explore accumulation and the relationship between an accumulation and derivatives
Accumulation: Need an Amount? (1-21-2013) An important and always tested application.
AP Accumulation Questions (1-23-2013) Two good questions for teaching and learning accumulation.
Graphing with Accumulation 1 (1-25-2013) Everything you need to know about the graph of a function given its derivative can be found using integration techniques. Increasing and decreasing.
Graphing with Accumulation 2 (1-28-2013) Everything you need to know about the graph of a function given its derivative can be found using integration techniques. Concavity.
Next Tuesday is Christmas (already). There will be no post until Tuesday January 1, 2019 when I will there will be several more links to post on accumulation.
Happy Holidays, Merry Christmas, and Happy New Year.