The Definite Integral Part II: Using Summation Notation to Define the Definite Integral

We quickly get through introducing summation notation to jump back into the big idea of computing the area under a curve as as a limit of a sum of rectangles.

Learning Objectives:
1) Express a sum using Summation Notation
2) Express the area under a curve as a definite integral

Now it’s your turn:
1) Summarize the big idea of this video in your own words
2) Write down anything you are unsure about to think about later
3) What questions for the future do you have? Where are we going with this content?
4) Can you come up with your own sample test problem on this material? Solve it!

Learning mathematics is best done by actually DOING mathematics. A video like this can only ever be a starting point. I might show you the basic ideas, definitions, formulas, and examples, but to truly master calculus means that you have to spend time – a lot of time! – sitting down and trying problems yourself, asking questions, and thinking about mathematics. So before you go on to the next video, pause and go THINK.

This video is part of a Calculus course taught by Dr. Trefor Bazett at the University of Cincinnati.

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