Can a function like this be integrated? It definitely has a lower
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Can a function like this be integrated? It definitely has a lower and upper bound on the total area enclosed by the graph.
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.
>>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.