Can a function like this be integrated? It definitely has a lower

yes! using the method of lebesgue integration

>>7969987
Depends. Are you talking about this Weierstrass function in particular, or non-differentiable functions in general?

Absolutely. In particular, the Weierstrass function has a trivial antiderivative that follows directly from the antiderivative of the cosine function.

>>7969995
Yes this one specifically, but it'd be cool to know about other continuous but not differentiable functions as well.

File: 1459073018103.jpg (97KB, 433x419px) Image search: [Google]

97KB, 433x419px

>>7969987
>asking cacl2 questions on 4chin instead of opening the book

>>7969987
well it's bounded from above and below, so it's lebesgue integrable on every bounded set.
not sure about riemann, but who cares

>>7970034
It's also continuous, so it's Riemann integrable. I think OP is mistaking integration for anti-differentiation, causing the question to appear confusing.

>>7970279
there's a difference?

>>7970303
If you just think of Riemann sums, then it's not at all surprising that this is integrable.