13 Mar
2014
13 Mar
'14
2:25 p.m.
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