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[tex]\int_0^{2\pi}{\cos xdx}=\left[\frac{\sin x}{x}\right]_0^{2\pi}=\frac{\sin 2\pi}{2\pi}-\frac{\sin 0}{0}=\sin - \sin = 0[/tex]

The sad thing is that the answer is actually correct. And afterwarts that person claimed that you should have gotten partial credit for getting the correct answers...

Here's another one: somebody claimed that

[tex]2(\log x)=(2\log) x[/tex]

because of associativity of the multiplication. I was sad all day after seeing this...

What are some of the most horrible math mistakes you've seen? It could also be instructive to students to see which mistakes not to make!