This week in AP Calc, we learned about integrals. An integral is used to find the exact area under a function on a set interval. This makes finding the area much easier and more accurate than using LRAM, MRAM, and RRAM. We also learned the rules to definite integrals and anti-derivatives. These rules were not hard and just seemed to be like the rules we learned for derivatives.
One big concept that we learned that I thought I would struggle with was the Fundamental Theorem of Calculus. This sounds like a scary thing, but once you use it a couple times, it becomes easy. It is a way to find the area under the function without having to use a calculator. All you have to do is find the anti-derivative of the function, evaluate it at the endpoints, and subtract them. Using the Fundamental Theorem of Calculus is way easier than doing the rectangle approximation and it also gives you the exact answer, not just an approximation. Another concept that I found interesting and useful was when we did the Desmos activity to figure out the equation to find the average height of the function on the interval. I think that that will come in handy in the future whenever I need to find an average area.
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February 2018
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