While Working on the Fundamental Theorem of calculus I used both inductive and deductive reasoning. At first while working out the problems I would try piecing together the information I thought I already knew and moved from there, this applied to learning how to apply the theorem and finding antiderivatives. This only worked about 25% of the time seeing as every three in four times I checked the solutions manual I was definitely very wrong. After that I started getting really knit picky and pulling out notes from chapter 3 as well as going over examples in the book over and over again just to make sure I finally understood what I was trying to tackle. The Fundamental Theorem of calculus is so fundamental because it shows the link between derivatives and integrals. Through it we can evaluate integrals exactly instead of trying to compute the limit of riemann sums. Through it was can also calculate area. The notation used connects to when we looked at integrals by themselves in chapter three along with u substitution in order to get a better grasp on antiderivatives.
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January 2018
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