Expert: Steve Holleran - 2/18/2007

Question
Is it true that:
(integral of x between negative infinity and 1) - (integral of x between 0 and positive infinity) = (integral of x between 0 and 1) ?

Improper integrals are outside the scope of my maths course but this came up in an exam question and I need to know if this is correct.

Thanks for your help.

Answer
Hi Simon,

Okay, this is not exactly my specialty either, but to the best of my recollection, when you break an "area" into integrals of other "areas", none of the integrals can be divergent.

Both of the integrals of x, from -inf to 1 and from 0 to +inf, are divergent improper integrals, so I don't believe that technically you can set up the equation you mention.

There is a pretty good explanation of this at sosmath.com, so maybe that would be of further help to you.

Sorry I couldn't be of more aid on this one.

Steve Holleran