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Calculus and Beyond Homework Help
Evaluate length of the spiral (Line Integral)
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[QUOTE="says, post: 5470873, member: 517464"] [h2]Homework Statement [/h2] Evaluate the length of the spiral with parametric equation ψ(t) =< 2 cost, 2 sin t, π/t >, with t ∈ [0, 2π]. [h2]Homework Equations[/h2] Line integral ∫[SUB]C[/SUB] f(x,y) dS [h2]The Attempt at a Solution[/h2] f(x,y) = z = π/t ∫[SUB]C[/SUB] π/t dS [0, 2π] are the lower and upper bounds of integration dS= √(dx/dt)[SUP]2[/SUP]+(dy/dt)[SUP]2[/SUP] ∫ π/t √(dx/dt)[SUP]2[/SUP]+(dy/dt)[SUP]2[/SUP] ; 0≤t≤2π Just wanted to check I've set this problem up correctly. At first I thought dS = √(dx/dt)[SUP]2[/SUP]+(dy/dt)[SUP]2[/SUP] + (dz/dt)[SUP]2[/SUP] and that I would just integrate that with respect to the boundaries. I don't think this is correct though. I don't really understand why though. [/QUOTE]
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Calculus and Beyond Homework Help
Evaluate length of the spiral (Line Integral)
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