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Today was our first official unofficial calculus class. You can take that how ever you want. So today we had a workshop class. We all received a worksheet with various antiderivative skill testing questions. A function that we had to antidifferentiate was:
While working on the questions, one question brought us to a lesson on finding the antiderivative of lnx.
The way to find it can be found on the slides, but I'll upload it anyways.
To find the antiderivative of lnx we used integration by parts. The processed used to find it is very ingenius. According to the LIATE rule from last class, we pick lnx as f because if we picked it as g' we couldn't antidifferentiate it. If we did why would I be going through this tutorial. Anyways. we chose lnx for f and for g', oh no there is nothing to pick. Oh yes there is, there is a 1, it's just that we don't write it because number multiplied by 1 is itself. Let's recap, f will be lnx, and g' will be 1. Differentiate lnx and then antidifferentiate 1. With that done, the rest is just applying the integration by parts.
In the end we derived a general formula for finding the antiderivative of lnx. It can be found on the slide. But I won't upload it because you shouldn't memorize it because it is better if you antidifferentiate by hand using the technique shown above unless you are Mr K and you've taught how to antidifferentiate lnx so many times that you remember it by heart.
That's all we did today. I don't know if that worksheet was for homework but I'd do it just in case. The next scribe will be zeph.
Good Night.
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