I think for me it made the most sense to do deductive reasoning. Knowing the rules gives me guidelines as I work on solving the problem. I can feel a bit lost when given a problem before the generalization. I do think both are important for different reasons and mixing it up, using both interchangeably is good because it forces you to think a little harder instead of just following a formula. It helps you actually understand versus memorizing the rule. Knowing that the antiderivative of the function is the area under the curve made things all connect. The fundamental theorem of calculus will help a lot as we work on problems about the area under the curve. It's fundamental and can be manipulated forwards and backwards since the antiderivative and the area relate to one another.
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March 2017
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