User:GFauxPas/Sandbox

Welcome to my sandbox, you are free to play here as long as you don't track sand onto the main wiki. --GFauxPas 09:28, 7 November 2011 (CST)

DiffEQ Ongoing Project
Assignment:


 * $\displaystyle \int_{\to 0}^{\to 1} \ln x \ln \left({1-x}\right)\ \mathrm dx$

So,

To do later: explain that continuity justifies switching sums and integrals

By induction:

Base case, $n = 2$.

Induction hypothesis, the $(n-1)^{\text {th}}$ case:

Inductive step, the $n^{\text {th}}$ case

... so

... is true for all cases $n \ge 2$, for $x \in (0\,.\,.\,1)$.

--GFauxPas (talk) 01:44, 25 March 2014 (UTC)