Integration defined or not

[horizon]

Hey, just wondering, if you integrate over an interval of [a,b], but between [a,b], the curve is discontinuous, then is the integral still defined?

Same question, if there is an asymptote between [a,b] but the integral is from a to b, then will it be defined?

Thanks in advance

[dc302]

First one, yes it is still defined.

Second one, technically no it is not defined unless the limit of the integral at the asymptote exists. If it does, it is called an improper integral. If it doesn't exist but both sides of the asymptote 'cancel' out, then it is still not defined but you can define something called a 'principle value' for the integral.

Also, any examples you have would be good.

[abeybaby]

what dc said, but with examples

[horizon]

Thanks!