No judgement, but you should know it’s not that simple. You can’t just pull out your calculator and add together an uncountably infinite collection of values one-by-one.
I mean, you could add together a finite subset of the values, which turns out to be the only practical way fairly often because a symbolic solution is too hard to find. You don’t get the actual answer that way, though, just an approximation.
The actual symbolic approaches to integrals are very algebra-heavy and they often require more than one whiteboard to solve by hand. Blackpenredpen “math for fun” on YouTube if you want to see it done at peak performance.
I mean they’re right, Leibniz used a modified s for summa, sum. And an integral is just a sum, an infinite sum over infinitesimal summands, but a sum nevertheless.
I get the feeling you haven’t solved many.
What a curious and needlessly judgmental reply!
No judgement, but you should know it’s not that simple. You can’t just pull out your calculator and add together an uncountably infinite collection of values one-by-one.
I mean, you could add together a finite subset of the values, which turns out to be the only practical way fairly often because a symbolic solution is too hard to find. You don’t get the actual answer that way, though, just an approximation.
The actual symbolic approaches to integrals are very algebra-heavy and they often require more than one whiteboard to solve by hand. Blackpenredpen “math for fun” on YouTube if you want to see it done at peak performance.
I mean they’re right, Leibniz used a modified s for summa, sum. And an integral is just a sum, an infinite sum over infinitesimal summands, but a sum nevertheless.