Fair enough! I obviously didn't bother to actually see if they were the same, I just saw the integral and the next step and was like, "Why does that look so complicated?"
My job doesn't use my math degree, so I spend a lot of time doing cost/benefit analysis of converting CI to construction factories vs converting CI to mines in the midst of a corundium crunch to see the limits that the economy can handle.
he, the semi-AAR makes an amusing read, and its nice to see some differential equations applied to analysis in Aurora. It would also have been fun to device a build-strategy that just barely makes use of the existing mineral stocks (i.e. so that the integral of the usage until break even plus existing stocks is just 0). Also curious to see the Federation dispersing its fighting assets so broadly, while seemingly little protection is retained on earth. Anyway, getting a bit off-topic here.
I realized the integral could be solved in a more elegant fashion, but I was worried that some readers might not be fully aware of some of the properties of integrals, so I just decided to solve the integral by presenting a solution that is easily verifiable using the chain rule, even if that meant spending more time using basic algebra to get a nice form in the end. Anyway; you solution is obviously more more elegant.
Theokrat thank you for that last explination, I was misreading what your were doing with Pother.
Glad we could clear this up then :-)
