I can't remember a fallacious proof involving integrals and trigonometric identities. My calc professor once taught us a fallacious proof.  I'm hoping someone here can help me remember it.
Here's what I know about it:


*

*The end result was some variation of 0=1 or 1=2.

*It involved (indefinite?) integrals.

*It was simple enough for Calc II students to grasp.

*The (primary?) fallacy was that the arbitrary constants (+ C) were omitted after integration.


I'm not certain, but I have a strong hunch it involved a basic trigonometric identity.

Here is my favourite: integrating by parts with $u=1/x$ and $v=x$, we get
$$\int\frac{dx}{x}=\frac1xx-\int x\Bigl(\frac{-1}{x^2}\Bigr)\,dx
  =1+\int\frac{dx}{x}$$
and "therefore" $0=1$.
Admittedly there is no trigonometry and so it's probably not the one you were looking for, but still...
