Like I mean all the integration rules for Calc 2, does this become useful later on? In upper division and grad school? I know we take lower divs for a reason, but I’ve noticed lower div is mainly computation and upper div is mainly theory/proofs (for all n, etc.) I suck at proofs and I have yet to take my first upper div, so idk.
Are these computations suppose to help us formulate proofs because we know how the integral works, as in do they help develop our intuition?
I ask this because I take my first upper divs next semester, so I plan on reviewing all lower div material, in hopes of easing the transition, but in my calculus book, not a single rigorous proof is offered.
I just finished my math BS this spring. Most math courses that I took after calculus that had calculus courses as pre-reqs wanted me to know what derivatives and integrals are and how they work but not necessarily know how to compute them. Differential equations was an exception, that one had me do some computations for both derivatives and integrals. My probability course used integrals but was only concerned with being able to set them up. Most of the time that I took an upper division course that required me to compute a derivative or integral, it would be intentionally made an easy function to work with since they want to test the upper division material and not your calculus ability (because your calculus ability was already tested when you took calc1 through whatever).
I took 4 proof courses: Discrete Mathematics, Linear Algebra (half proofs, half computation), Number Theory, and Intro to Real Analysis. Real Analysis was the only one of these for me that went in depth with derivatives and integrals (as well as limits) and really required that you understood how they work and what they mean. It did not require me to do any difficult computations though.