Find the length of the spiraling polar curve:
8e^1theta From 0 to 2pi
Length=?
8e^1theta From 0 to 2pi
Length=?
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L = ∫ √(r^2 + (dr/dθ)^2) dθ
...= ∫(θ = 0 to 2π) √((8e^θ)^2 + (8e^θ)^2) dθ
...= ∫(θ = 0 to 2π) 8√2 e^θ dθ
...= 8√2 e^θ {for θ = 0 to 2π}
...= 8√2 (e^(2π) - 1).
I hope this helps!
...= ∫(θ = 0 to 2π) √((8e^θ)^2 + (8e^θ)^2) dθ
...= ∫(θ = 0 to 2π) 8√2 e^θ dθ
...= 8√2 e^θ {for θ = 0 to 2π}
...= 8√2 (e^(2π) - 1).
I hope this helps!