Tried changing variables and also per parts but I may be impatient. Any advices/solution ?
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Anonymous2008-12-19 18:13
Can't be done without elliptic functions. Are you sure you read the question right?
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Anonymous2008-12-21 16:59
In fact it's a part of a question. We have the curve in R^3 defined by gamma(t) = (0, t, t^4). I want to get the parameter s(t) which is the arc's length (I don't know the term in english). For this you must integer the euclidian norm of the gradient : the gradient is gamma'(t) = (0, 1, 4t^3) and its norm is sqrt(1+16t^6) (I failed to copy it correctly when I started the thread).
The complete question is : let S be a revolution surface; we can parametrize this by f(u,v) = (p(v)*cos u, p(v)*sin u, q(v)) where p and q are at least C^2 regular functions.
We are given the curve z = y^4. Question : is there a way to paramtrize REGULARLY the surface S generated by this curve ?
I parametrized the curve by gamma(t) = (0, t, t^4)... I think q(v)willebe equal to v and p(v) equal to v^4 (with v=y) BUT I must have the arc lenght if I want to do the next questions (one is to determine the secondary fondamental form of this surface)
See the problem ? Or am I completely misunderstood ?
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Anonymous2008-12-21 18:58
>>3
I dunno lol, but Maple sez you can't integrate sqrt(1+16t^6) either.