- "In learning about the fundamental theorem of calculus, what type of learning did you primarily rely on, deductive or inductive? Or did you rely on both? Be specific! Also, explain why you believe the fundamental theorem of calculus is so fundamental? In your mind, what does it mean, what are it’s implications, and how does it fit in the context of calculus broadly?”
- Whenever I learn something new, I like to look at other examples to see how it is done. I also like having a set of rules to look at when doing said problems. I used these approaches when learning the fundamental theory of calculus. So I guess I used both inductive and deductive reasoning. to understand what the fundamental theory of calculus is all about. I like doing the activities before going over notes. It helps me get an idea of what we are doing. But with the notes, I like to look at the theorems and rules to understand the concepts. This concept is a huge one in calculus because it brings all the concepts that we have been learning into one idea. The definition of the fundamental theorem of calculus (as of Wikipedia) is a theorem that links the concept of the derivative of a function with the concept of the integral. The first part tells us "that the definite integration of a function is related to its antiderivative, and can be reversed by differentiation”. The second part tells us “that the definite integral of a function can be computed by using any one of its infinitely many antiderivatives”. These concepts show us how the past few chapters really fit together.