A useful integral for kids learning calculus

My son is in the middle of a long review for the BC Calculus exam in May. Right now he’s doing some integration practice and came across this integral today:

We didn’t get a chance to talk about it too much this morning, but we did review the problem when he got home tonight.

First we I asked him to approach the problem as he did this morning -> by trying to evaluate the integral. The practice integrating rational functions turned out to be useful:

Next we took a more geometric approach:

Finally, I wanted to show him how you could see that the integral was zero from the u-substitutions that he made in the first video. Even though this method wasn’t really the best one for this particular integral, I still wanted him to see how the algebra worked out:

2 thoughts on “A useful integral for kids learning calculus

  1. hey Mike (sorry, not about the post), just wondering if there is still a way to “search” your blog postings? I was looking for anything you may have blogged (or even written elsewhere) re: ‘March Madness’ contests/statistics, either in general or your own specific involvement…

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