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- Summary
- Some questions/thoughts on the fundamental theorem of calculus?

As you can see form my previous posts, I am in my first university level calculus class ever. It is going very well, and through the class I am asking good questions and trying to actually make connection with the stuff we arr doing - not just doing the math just for the sake of passing - I am actually interested in math.

So, let me set it up for you. We began talking about limits (and everything that goes with them) and then we started with derivatives (and everything that goes with them) and then chain rule and then applications of this/related rates and then we studied integrals. All of this was leading up to her telling us about the fundamental theorem of calculus....that was today.

I was thinking to myself before class today "okay, here it is, I am going to have this big ah-ha moment when i put it all together". Then we were told what the theorem is. Needless to say, I was disappointed. I found out that the theorem basically says that taking a derivative is the inverse function of taking an integral and vice versa. If that is not correct, then please correct me.

The reason I am disappointed is because during the class time when we started talking about integrals and how to do them, it becomes fairly obvious that it is the opposite of taking a derivative. What I mean to say is way back when the founders of calculus came up with this theorem it must have been a HUGE deal to discover this because today when you see it after doing derivatives and integrals it is sort of like "duh, yeah". My question is, did this stump the fathers of calculus at first? Were they confused on what is the opposite of a derivative is? Today when you see it after taking a calc class, it is no more surprising than figuring out multiplication is the inverse or dividing or likewise with addition/subtraction. My question is was it a big mystery to the founders of calculus?

So, let me set it up for you. We began talking about limits (and everything that goes with them) and then we started with derivatives (and everything that goes with them) and then chain rule and then applications of this/related rates and then we studied integrals. All of this was leading up to her telling us about the fundamental theorem of calculus....that was today.

I was thinking to myself before class today "okay, here it is, I am going to have this big ah-ha moment when i put it all together". Then we were told what the theorem is. Needless to say, I was disappointed. I found out that the theorem basically says that taking a derivative is the inverse function of taking an integral and vice versa. If that is not correct, then please correct me.

The reason I am disappointed is because during the class time when we started talking about integrals and how to do them, it becomes fairly obvious that it is the opposite of taking a derivative. What I mean to say is way back when the founders of calculus came up with this theorem it must have been a HUGE deal to discover this because today when you see it after doing derivatives and integrals it is sort of like "duh, yeah". My question is, did this stump the fathers of calculus at first? Were they confused on what is the opposite of a derivative is? Today when you see it after taking a calc class, it is no more surprising than figuring out multiplication is the inverse or dividing or likewise with addition/subtraction. My question is was it a big mystery to the founders of calculus?