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I was and am bad at integration problems like this. I find them scary. And mysterious. Somehow I associate these with engineering type classes, but that may not
by zwaps 5y ago
I was and am bad at integration problems like this. I find them scary. And mysterious. Somehow I associate these with engineering type classes, but that may not be generally true.
On the other hand, I really enjoyed and did well in classes like real analysis, functional analysis and measure theory, even though I am not a mathematician.
But those classes are fun. Say, the construction of measures and Lebesgue type integrals makes sense to me.
Integration by parts? And this stuff? I feel like a stupid monkey.
It's weird.
For a real mathematician, both of these types of skills are probably important.
I wish I could do integrals better.
- javajosh 5y agoThey are just games with symbols. But yes, some moves are scary. The moves that scare me are those whacky out-of-nowhere algebraic additions that lead to a simplification later. They are scary because somehow someone anticipated that one addition out of an infinity of possibilities would be useful "down the road" in the computation. (This is done a couple of times in the OP's integral.)
- zwaps 5y agoI think it is interesting that some notions in this thread boil down to the idea that this ain't real math like, say, real analysis. In my limited view, many proofs are easier. Especially easy ones that are (if that makes sense) more sequential in the required thinking. I think there is a lot of cleverness in these integral calculations, a lot of creativity to, as you say, come up with some seemingly nonsensical transformation that down the road turns out useful. Perhaps it's because I am so bad at it, but I find people who does this easily very impressive. I feel the same way for differential equations, where, incidentally, I also suck. I wonder whether anyone ever did a study on the cognitive skill "dimensions" in maths.