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.

The simplest one I have is not actually 0=1 but $\pi=0$. This is one of my favourites,the most shortest and has confused a lot of people.
$\int \frac{dx}{\sqrt{1-x^2}} = sin^{-1}x$
But we also know that $\int - \frac{dx}{\sqrt{1-x^2}} = cos^{-1}x$
So therefore $sin^{-1}x=-cos^{-1}x$
But also, $sin^{-1}x+cos^{-1}x=\pi/2$
$\implies \pi/2=0$ $\implies \pi=0$.
I'm so evil. :)
