Like most math books, my calculus book gives the answers to the odd-numbered problems in the back and consequently, my instructor only assigns these problems when (1) the question is proofy and there is no answer in the back of the book or (2) the problem is so hard that seeing the answer probably isn't going to help you get there.
Yesterday I was working on an awkward improper integral with an integrand that is undefined at both limits of integration, which I didn't (and still don't) really know how to deal with, and my first stab at the problem yielded the implausible answer: -1/2 ln (i). Hmm. But hey, it's an odd-numbered problem - maybe I'll look up the answer and it will say "divergent." Nope. The answer is pi. I may not be able to understand what the natural log of the square root of negative one could possibly be, but I do believe it is unlikely to bear any relationship to pi. Oh well. My confusion on this question was such that I pulled out my old textbook from college and read the section on improper integrals, which is either much clearer and better written, or I learned more from my current textbook than I thought. Unfortunately, its straightforward explication of the improper integral did not extend so far as to make clear what to do when both limits are screwy.
Once again, it's as though my book expects me to so deeply understand the material that I can extend it under my own brain power. What do they take me for? A math major? Screw them and the logic system they rode in on!
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4 comments:
OK, I'm an idiot, but I have it right now. e to the power of (i * pi) is -1. I knew I had it in me somewhere.
Yeah, Google calculator tells me that my answer =
- 0.785398163 i (-1/4 pi * i)
So my answer, though totally wrong, is still less crazily wrong than I originally thought, and does bear some relationship to pi. This is a small comfort, I suppose.
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