While learning the Fundamental Theorem of Calculus, I believe that I used a mix of both deductive reasoning, and inductive reasoning. I think I used more deductive reasoning than inductive reasoning because the topic felt more complex for me. It was easier for me to do a couple problems, and conclude that the Theorem was true, because by plugging in the numbers into the Theorem, I got an answer that made sense in the context of the problem. I started with the Theorem, and understood it by using data to show that the Theorem did in fact work.
I believe that this is a fundamental part of Calculus because it links derivatives and integrals together. Without it, we would have no truly accurate way to figure out the area under a function. This helps with evaluating the area, not just estimating it. I think that the notation of the integrals was not that difficult because all of the notation except the actual integral sign has been already used. We know what a function is, we have seen dx at the end of functions, and we know about intervals. The only thing that confused me at first was when you find the antiderivative and you used the line to show that you evaluate at the bounds.
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February 2018
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