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anonymous
 5 years ago
Find the length of the curve given by
r (t) = ((2^0.5)/2) t)i+(e^t/2)j+(e^−t/2)k,
where −2 =< t =< 7.
anonymous
 5 years ago
Find the length of the curve given by r (t) = ((2^0.5)/2) t)i+(e^t/2)j+(e^−t/2)k, where −2 =< t =< 7.

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0okay  so let me take a shot at it. Since you are given a function r(t) in terms of all vector component, what needs to be done is to take partial derivatives of each components in terms of t. Then square each terms and add them, put the sum of squared partials under square root and integrate over the range of t then that should be the length of your curve.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i did that and got ((1/2)+(1/4)e^t+(1/4)e^t )^(1/2) so i have to integrate that.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0that would be something like... \[s = \int\limits_{t_{i}}^{t_{f}} \sqrt((\delta x/\delta t)^2 + (\delta y/\delta t)^2 + (\delta z/\delta t)^2)) dt\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0something along this line

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0be sure that dt is not under square roots
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