Tag Archives: khan academy

Videos: Integration by Parts, Trigonometric Integrals, Trig Substitutions

In order to learn the various methods of integration, you need to you read, see, and work through as many examples as you can. That’s why I’ve urged you to take notes in class, read the examples in the textbook, try to do all the homework exercises, and ask questions about any examples and exercises you are confused about.

Here are more examples for the various methods of integration we’ve covered in the past few weeks:

Integration by Parts

Khan Academy’s IBP sequence

PatrickJMT’s first IBP video (see the list of all his calculus videos here!):


Trigonometric Integrals

Trigonometric Substitutions





Visualizing Riemann Sums: Visual Calculus, Wolfram MathWorld, Khan Academy

We won’t spend much time in this course studying Riemann sums and the formal definition of the definite integral, but I encourage you to read the relevant parts of the book (Sec 5.1 and the first part of Sec 5.2) and try to understand the concept.

You can play around with the “Visual Calculus” visualization of Riemann sums I showed in class on Monday. There are a number of such visualizations on the web; for example, take a look at Wolfram MathWorld’s Riemann sum page.

Khan Academy has a sequence of 10 short videos on Riemann sums which you may find helpful. Here is the first one:

Khan Academy’s Integral Calculus Videos: “Antiderivatives and indefinite integrals”

As I mentioned during our first class meeting yesterday, there are numerous resources that you can take advantage of to help you learn the material. Of course there are on-campus resources such as my office hours and the tutoring centers (more information on that will be provided soon!).  But there are also numerous online resources–a popular one is Khan Academy.

Here is the link to their Integral Calculus sequence of videos. Try taking a look at the first one, which starts with the same topic we started with yesterday:
Antiderivatives and indefinite integrals

Khan Academy’s videos are also on YouTube, which may be useful in case you want to watch on your phone or on a tablet:


Let me know if you find these videos useful (you can always leave a comment below). And of course let me know if you have any questions about the math!