In calculus this week we learned a whole bunch of things! First we learned about definite integrals and anti-derivatives and all their rules, including the sum and difference rule, the additivity rule, and the domination rule. The rules are all pretty straightforward and follow common sense, so I feel pretty good about them. The only thing that I have to remember is one part of the sum and difference rule. When you take the integral of the sum or difference of a function and a constant, that constant acts as its own linear function and you have to use the function rule. This was one of the questions I got wrong on the AP practice quiz that we did in class. This week we also learned about finding the average value of a function on a closed interval. We started this by doing a lab. I got the concept of what is above the average equaling the distance of values below the average, but I didn't get to the formula for finding the average value of a function. It makes sense, I just couldn't get it on my own. The final thing we learned this week (and seemingly an incredibly important and crucial concept in calculus!! Our math lives have been leading up to this point!! I am not really sure why exactly it is so important but that's the vibe I was getting.) was how to find the definite integral with anti-derivatives. This one was kind of confusing and hard to follow during the notes but once I was doing it in the homework it just clicked and started making sense. Yay!
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Josephine Swaney's AP Calc Blog Archives
January 2018
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