The Definite Integral Part III: Evaluating From The Definition

Description: Our final step is to actually fill in the formula and evaluate the limit

Learning Objectives:
1) Set up and evaluate a definite integral from the definition

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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[leadersheir]

"Two over six, the last time I checked, was just equal to the value, of one-third" 🤣🤣🤣
One of the BEST teachers I've ever seen.

[Sisyphussa]

I don't know if it's just a coincidence or this holds some merit, but if you go back to the rectangle method and compute it in two different ways (the right and the left end of the rectangle touch the curve) and you average it out, it gives back 0.34, which is pretty darn close to 1/3.

[naiko]

You made the integral start from 0 to 2, i think for simplicity sake. However, in this way, it's not clear that 'xi' is NOT just i*deltax but actually xi = a + deltax ...because, of course, we start computing the points from a

[mubahaliqbal]

Sir, plz give a lecture on mass and moment of inertia