find the lenght of the curve at u= t^3/6, v= t where t is from -1 to 1
and E = 1, F=0 and G= 1+v^2.
do we find it from t =0 to 1 and then multiply it by 2? because if i were to integrate it from -1 to 1, then it would cancel each other out.
find the lenght of the curve at u= t^3/6, v= t where t is from -1 to 1
and E = 1, F=0 and G= 1+v^2.
do we find it from t =0 to 1 and then multiply it by 2? because if i were to integrate it from -1 to 1, then it would cancel each other out.
The length of a vector, <u, v>, on a surface with that first fundamental form would be
So you want to integrate
You can factor out a to get
Because that, like any "metric" integral involves only even powers, the integral from -1 to 1 cannot be 0. The integrals from -1 to 0 and from 0 to 1 will add, not cancel.