I agree with Brent's suggestion. I’ll add that the usual way of writing an indefinite integral as "F(x) + C" leaves it quite unclear to the average student that this stands for the *set* of functions {F(x) + C | C in R}. And as I think I’ve mentioned before, this is particularly confusing in cases like the claim (*) Integral (1/x) dx = ln|x| + C , which misleadingly imply the set of indefinite integrals is 1-dimensional. I maintain that (*) is just plain wrong. —Dan On Mar 13, 2014, at 1:48 PM, meekerdb <meekerdb@verizon.net> wrote:
"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?
What does C represent?