Behind every definite integral is a Riemann sums. Students need to know about Riemann sums so that they can understand definite integrals (a shorthand notation for the limit if a Riemann sum) and the Fundamental theorem of Calculus. Theses posts help prepare students for Riemann sums.
Integration Itinerary Some thoughts on the order of topics in your integration unit.
Some preliminary posts leading up to Riemann sums
- The Old Pump Where I start Integration
- Flying into Integrationland Continues the investigation in the Old Pump – the airplane problem
- Jobs, Jobs, Jobs Integration in real life.
- Working Towards Riemann Sums (12-10-2012)
While I prefer to teach antidifferentiation after students have learned about the Fundamental Theorem of Calculus, others prefer to discuss antidifferentiation firsts and the topic often precedes Riemann sums in textbooks. (See Integration Itinerary ) If you are among those, here are posts on antidifferentiation. If you teach this topic later, save this post for then.
ANTIDIFFERENTIATION
Antidifferentiation (11-28-2012)
Why Muss with the “+C”? But still don’t forget it.
Arbitrary Ranges (2-9-2014) Integrating inverse trigonometric functions.
ANTIDIFFERENTIATION BY PARTS This is a BC topic, or you could use it after the exam in an AB course.
Integration by Parts 1 (2-2-2013) Basics
Integration by Parts 2 (2-4-2013) The Tabular Method
Modified Tabular Integration (7-24-2013) A quicker way
Parts and More Parts (8-5-2016) Reduction formulas (Not tested on the AP Calculus exams)
Good Question 12 – Parts with a Constant (12-13-2016) How come you don’t need the “+C”?
