Sharing a fun calculus example from John Carlos Baez with my son

Saw a neat tweet from John Carlos Baez last week:

It was an nicely timed tweet for me because my son is beginning a long review of calculus ideas this year. Tonight I finally got around to sharing the idea with him.

We began by talking about some basic properties of the function:

Next we talked about how you could approach integrating the function and then used Mathematica to help with the polynomial division:

Finally, we went to the whiteboard to work through the integral and talk about the nice surprise:

I really like this integral. It is both a neat “fun fact” and a great example to share with kids learning calculus.

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