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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: horizon on November 07, 2011, 09:43:15 pm

Title: Integration defined or not
Post by: horizon on November 07, 2011, 09:43:15 pm

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

Title: Re: Integration defined or not
Post by: dc302 on November 07, 2011, 10:13:58 pm

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.

Title: Re: Integration defined or not
Post by: abeybaby on November 07, 2011, 10:15:12 pm

what dc said, but with examples :)

Title: Re: Integration defined or not
Post by: horizon on November 08, 2011, 08:10:27 am

Thanks!