is the infinite integral of an oscillating function like sin(x) or cos(x) 0? i know that a definite integral of this type will depend on the limits of integration, but over the interval [0, infinity) 0 seems like the only thing that would make sense but i wanna convince myself a little more strongly than that
The integral is undefined,
say for sin(x)
if we take the limit as cos(a) approaches infinity we see it cant converge, if we add some more to a, the integral would always change value it doesnt settle down to just one value over time (crap explanation I know, but I hope you get the gist of what I'm saying!)
hey, if you or anyone else knows of a good book that talks about these kinds of mental issues (the ones i have) let me know! thanks!
I am not sure that I can give a clearer explanation. Just remember that when it comes to the infinite, you need to leave your intuitions and preconceived notions behind, because things will often have unexpected results.