As long as you don't cross the singularity at 0, G. B. Thomas is correct. Assume b > a > 0. int(1/x, x=-b..-a) = -int(1/x, x=a..b) = -log(b/a). log|-a| - log|-b| = log a - log b = -log(b/a). If you do cross the singularity, then in integral has no well defined limit. -- Gene
________________________________ From: Dan Asimov <dasimov@earthlink.net> To: math-fun <math-fun@mailman.xmission.com> Sent: Tuesday, February 4, 2014 4:53 PM Subject: Re: [math-fun] More 4th grade "math"
One error I believed for many years* is that the antiderivative of 1/x is ln|x| + C.
--Dan ______________________________________________ * Thanks to my misplaced trust in G.B. Thomas.
On 2014-02-04, at 2:59 PM, James Propp wrote:
Someone should write a book for college teachers that explains what misinformation students commonly carry with them when they arrive at college.
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