/sci/ - Science & Math

>>10214813
Only integrating I do

What is an integral?

I took AP Calculus AB (basically Calculus I) in high school so I started my first semester of college with Calculus II. Entering with the mentality of "Calculus II can't be much harder than Calculus I", I didn't pay much attention in class. I just got my final exam back and ended up with a 84% overall grade in the class. I was really stressed out the past few weeks because I was afraid I would have to repeat the class. I'm taking Calculus III next semester and I don't want to be in the same situation where I'm extremely stressed right before exams. I have three weeks of Winter break and want to spent a few days or a week "previewing" Calculus III material. Where do I start? Also, what are some Calculus III/general math tips for doing well?

How do I quickly memorize trigonometric substitutions, identities, and common values quickly? My test is on monday.

Can it be defined that an integral with infinite area is smaller than another integral with infinite area?

Integrals can be "sharp" (converging) or "open" (diverging) and it would seem rational that a "sharp" integral is in most cases smaller than an "open" integral. Just think about their shapes - a sharp one, like that of 1/x will keep getting smaller and smaller as x grows while an open one, like that of x^2 will keep growing. How isn't the integral area of x^2 larger than that of 1/x?
Can any generalizations be made of this?

>>5752193
>that integral sign
He doesn't deserve to win shit.

Let me give you a hand with that.