Would you say that integration is harder than differentiation in general for most functions, or would you say that they are the same difficulty? Or, would you say that humans are not as good as differentiation?

Question

inkyvoyd · Answer

Or would you say something different altogether? and what would that be?

anonymous · Answer

I think this will help you http://betterexplained.com/articles/calculus-building-intuition-for-the-derivative/

inkyvoyd · Answer

kalid's comment on that link was quite helpful.

anonymous · Answer

Yeah I really liked his explanation

inkyvoyd · Answer

But, in general, I usually find the antiderivative quite difficult. However, it is essentially very similar to the derivative right? I heard from somewhere that Leibniz started from integrals, while Newton started from tangent lines?

anonymous · Answer

Maybe it's because derivative has a specific definition.But we define integral as just anti derivative.So we have to do a lot of guessing most of the time

inkyvoyd · Answer

But is all of the guessing necessary?

inkyvoyd · Answer

Or is it more like the difference between reading backwards text backwards and reading normal text normally?

anonymous · Answer

You kinda have to because it's the only way we defined integration as

inkyvoyd · Answer

Aren't there functions, like integration, with no derivatives that have an elementary expression?

anonymous · Answer

Didn't get you.What do you mean

inkyvoyd · Answer

I mean, there are some functions that apparently don't have an elementary function expression when we integrate them (like erf() maybe?); there are functions that are the same when we derive them, right?