And outside really. Don't tell my best friend Jo B, but I "have yet to" [i.e. can't] understand calculus. If I were in a battle and I was propositioned with "Give Me Calculus or Give Me Death," it was nice knowing you.
So I activated my growth mindset and after another failed attempt of understanding any form of calculus thought, I said to myself "Lulu, you are capable of understanding this and you WILL get a deeper understanding." Here I am, back at it again. First, I went to dummies.com to try to explore The Fundamental Theorem of Calculus for dummies.
Here is my now [much deeper] understanding of the (1st) FTC:
- It's important. Phew! That was a tricky one at first. You did it! Press on...
- Then... we have a function "f(t)", okay I'm totally with you. The function creates a line on our graph.
- Now... they want me to find the area under the curve? This is called F(x). So this F(x) IS the area under the "curve" or the function. I still feel okay, pending I'm not completely wrong.
- Now, the area that we are measuring starts at value a and ends at value x. Makes sense.
- Now I'm getting lost... dt represents the derivative of f(t) which is the amount that it is increasing or decreasing?
- And that's it!
- Okay... so now we tackle the 2nd FTC, which I guess solves for all definite integrals? Well they switched me from f(t) to f(x) but I guess they're the same thing? Also, F(b) - F(a) is apparently F(x) evaluated from a to b... but where did b come from? Now I am lost. But hey! I got through at least half of the explanation without crying. I call this a win all around.