How do I show that the arclength of Bernoulli's (unit) lemniscate is 2p, using the formula r^2=cos(2t) for the lemniscate.
Note: p is given by the integral p=int_{-1}^{1} dt / (1+t^4)^(1/2)
Thanks in advance,
Ourubo
P.s.:
Bernoulli's lemniscate is defined for example on http://mathworld.wolfram.com/Lemniscate.html
Note: p is given by the integral p=int_{-1}^{1} dt / (1+t^4)^(1/2)
Thanks in advance,
Ourubo
P.s.:
Bernoulli's lemniscate is defined for example on http://mathworld.wolfram.com/Lemniscate.html