I imagine "what is the sea" would give it away and "don't confuse different variables for each other" would confuse half and give it away for the balance. Have you tried waving your arms around and shouting, "MATH IS BROKEN!"? Charles Greathouse Analyst/Programmer Case Western Reserve University On Thu, Mar 13, 2014 at 4:24 PM, James Propp <jamespropp@gmail.com> wrote:
I just invented this paradox, though I doubt I'm the first:
"On the one hand, the indefinite integral of 2x+2 w.r.t. x is x^2 + 2x + C; on the other hand, putting u = x+1, we can write the integral as the integral of 2u w.r.t. u, which is u^2 + C = x^2 + 2x + 1 + C. Equating x^2 + 2x + C with x^2 + 2x + 1 + C we get 0 = 1."
Here's my question for you guys: For those students who are stymied by this paradox, what would be a good hint? I've tried "Think about what indefinite integration IS", but that just seems to confuse them more. Is there a good hint that doesn't give away the game?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun