-2
$\begingroup$

There must be an error in this partial integration but I do not see it. Do you see it?

enter image description here

$\endgroup$
1
  • 6
    $\begingroup$ This is not a question about math education. It is a question about mathematics. $\endgroup$ – Sue VanHattum Nov 29 '20 at 19:09
4
$\begingroup$

The term in parentheses in the middle expression should be the change in $x\frac{1}{x}$ from $x = 1$ to $x = 2$ (which evaluates to zero), not just $x\frac{1}{x}$ (which evaluates to $1$).

But as @SueVanHattum says, we are here to defend mathematics education, not to practise it.

$\endgroup$
4
  • 1
    $\begingroup$ Although I wasn't seeing the error in this intriguing question, I had thought we probably shouldn't answer it, as it may be a graded exercise in a course. $\endgroup$ – Sue VanHattum Nov 30 '20 at 3:24
  • 1
    $\begingroup$ @SueVanHattum Interesting point. On other SE sites where I participate, the policy is that "homework questions" are considered on-topic only if the OP shows what efforts s/he has made to answer the question independently, and I thought OP in this case had met this condition (assuming that the original homework question was "compute the integral", not "find the error"). $\endgroup$ – Daniel Hatton Nov 30 '20 at 11:28
  • $\begingroup$ If the homework question had been "compute the integral", I wouldn't expect to see anyone use integration by parts. That's why I assumed it was "find the error". (Thanks for giving me more info about the typical SE policy. On this site, we rarely deal with questions that could be homework, since they are math not math education, and I don't use other SE sites much.) $\endgroup$ – Sue VanHattum Nov 30 '20 at 18:24
  • $\begingroup$ @SueVanHattum Why not? That particular integration-by-parts trick would work a treat if the integrand were $1/x^n$ with $n > 1$, so it's fairly natural to give it a try when the integrand is $1/x$. $\endgroup$ – Daniel Hatton Dec 1 '20 at 22:56

Not the answer you're looking for? Browse other questions tagged or ask your own question.