The integral |

I was chatting with the students in the last couple of minutes of class, and I showed them the TI-92 calculator emulator that I have on my laptop. When I did the integral on the calculator, this is what I got.

Output from VTI |

When I got back to my office one minute later, I sat at my desk and the answer hit me. The factor of 1/4 was absorbed by the arbitrary constant as follows.

Now I see! |

So, the arbitrary constant comes back to get us again. That is why math teachers are so picky about it.