User talk:Mathleeet

Witch of Agnesi centroid
Hello. I reverted [//en.wikipedia.org/w/index.php?title=Witch_of_Agnesi&diff=635334911&oldid=625428467 your edit] because as discussed by the source, there is not a well-defined centroid to this region. The centroid would be defined as $$\frac{\int_{-\infty}^{+\infty}\frac{x}{1+x^2} dx}{\int_{-\infty}^{+\infty}\frac{1}{1+x^2} dx}$$. However, the integral in the numerator is not a well-defined improper integral. Using the fundamental theorem of calculus evaluates it to $$\lim_{(a, b)\to(-\infty,\infty)} \frac{1}{2} \ln\frac{1+b^2}{1+a^2}$$. This limit does not exist (it is not enough for the Cauchy principal value to exist) and so in spite of intuition, rigorously one cannot define a centroid for the region between the x-axis and the witch of Agnesi.--Jasper Deng (talk) 09:35, 12 July 2015 (UTC)