find the volume of the unlimited solid obtained by revolving y=1/(x^4 +1) around its asymptote, show work.
helllpp pleaseee, I have no idea how to do this...
The asymptote is y=0
So, revolving the area around the x-axis, and using symmetry,
v = 2?[0,?] ?y^2 dx
= 2?[0,?] ?(1/(x^4+1))^2 dx
= 3?^2/(4?2)
It looks hard, and it is complicated, but you can start off by noting that
x^4+1 = (x^2+1)^2 - 2x^2
and then factor that as the difference of squares. Then you have to resort to trig substitutions. See
http://www.wolframalpha.com/input/?i=%E2%88%AB(1%2F(x%5E4%2B1))%5E2+dx