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.