Mike Lawler Inspired Integration

Back in March I saw the tweet shown below from Mike Lawler (@mikeandallie).

Screenshot 2019-05-28 01.06.07

I think I would default to substituting \( u = \mathrm{e}^x \) here but in the thread were a range of different approaches. Tim Gower’s (@wtgowers) was particularly inventive.

I’ve always enjoyed asking students to integrate things in different ways and then asking them to show their solutions are equivalent. A favourite one of mine is \(\int \sin(x) \cos(x) \ \mathrm{d}x \). Because of this I have made a sheet asking students to explore a few of the possible methods.

The sheet for printing to A3 can be downloaded here.

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