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Find the length of the curve ; r (t)=<2t^3/2 , cos (2t) , sin (2t)>, 0<= t <= 3. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals.
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The Length of Curve Calculator finds the arc length of the curve of the given interval. The curve length can be of various types like Explicit, Parameterized, Polar, or Vector curve.
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Find the length of the curve r. ⃗. (t) = 2–√ ti^ + 2–√ tj^ + (1 −t2)k^ from (0, 0, 1) to ( 2–√, 2–√, 0) Solution Attempt: First find the arc length function for this vector by using s(t) = ∫||r′(t)||dt. Where r′(t) = 2–√ i^ + 2–√ j^ − 2tk^ and ||r′(t)|| = 2 1 +t2− −−−−√.
