So ye... I am enthusiastic 11th grade student who wants to learn integrals for personal reasons. What other aspects do I need to know before starting?
Lol, enthusiastic. Well, if you're ahead of your peers then I suppose I understand your current opinion on your status. Anyway, if you know what a derivative is and don't want the theory, then you're fine. If you want the theory, you should probably understand some set theory, a very small bit of topology, and limits.
What is a single-variable analog of Marsden/Tromba's textbook? Stewart or there is something "stronger" (but not Spivak, Apostol or Courant)?
Anyway, has anybody read pic related?
Step 1. Get stewart calculus.
Step 2. Read, take notes, practice, understand.
Step 3. Get a more proof based book and study that, or you could do this right at the beginning but this depends on your skill and what you have learned so far.
I taught myself basically all of calc until infinite series in 11th grade by just watching khan academy and OCW videos. Just do that shit, find some practice problems online, and you'll be fine.
All you really _need_ to understand the definition of an integral and how to evaluate them is a bit of high school algebra.
If you want to use them for anything much you'll need to be comfortable with trig and also know what a derivative* is.
*doing derivatives before integrals isn't strictly necessary, if you don't want to for some reason; some books (like Courant) develop integrals first.
It's just standard practice nowadays to teach differentiation before integration.
Integral of the Circle's length is half the Disc's Air:
Circle length = Pi.D
Air of the disc = 1/4.Pi.D2
(like in the relation ax^n -> anx^(n-1))
[spoiler]That little thing blew my mind when I was a kid... cant remember exactly why btw.[/spoiler]