In learning the fundamental theorem of calculus I relied on both deductive and inductive reasoning. I did find it easier to use inductive reasoning more than deductive reasoning, just because it was easier to grasp what is being talked about. I usually learn better by seeing and then doing rather than being thrown a bone and left to fend for myself when being introduced to a new idea. I am able to learn on my own, but I do struggle when things are assumed to be understood and I don’t completely grasp the idea. As a dancer I am able to see what I am supposed to be doing and then I can recreate it myself. I have found over the years in math that once I have seen a certain type of problem I can do them and build upon them, I just need to see a basic example to get myself going.
The fundamental theorem of calculus is so fundamental because it shows that every continuous function has an antiderivative, that the process of integration and differentiation are inverses of one another, and that definite integrals can be evaluated directly from the antiderivative of a function. Because this is known then you are able to find the integral of an equation much easier
In my mind the fundamental theorem of calculus is still a little fuzzy. At times I completely understand it, but at other times I am completely lost. I know that it really is allowing for the area under a curve to be found, but it still is slightly difficult to grasp.