DP is basically brute-force but you can reuse some of the subproblems.
Another approach is trying to find a "starting point" and solving subproblems. Imagine an array of problems and starting at the left.
Another approach is trying to find a "starting point" and solving subproblems. Imagine an array of problems and starting at the left.
this is like saying
"integration is basically weighing a bunch of buckets but the buckets are really small"
cool but that won't help you find the correct trig sub to perform the integral. anyone that's familiar with the calc grind knows getting a good grade for the anti-derivative (indefinite integral) module is about the number of exercises you've done rather than the conceptual understanding.
> cool but that won't help you find the correct trig sub to perform the integral. anyone that's familiar with the calc grind knows getting a good grade for the anti-derivative (indefinite integral) module is about the number of exercises you've done rather than the conceptual understanding.
I am a mathematician and teacher of mathematics.
Understanding the first point is way more valuable than teaching the second. I have to ask and grade trigonometric-substitution problems for my Calculus II class because the curriculum includes it, but I'd way rather have a student come out of my class with a solid understanding of why your quoted statement about integration is true than to be able to find just the right substitution but have no idea why. They can look up the trigonometric-substitution stuff when they need it.