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Find the arc length L of the curve C given parametrically x equals 1 plus 2et y equals et 0 t1?
Wiki User
∙ 9y ago
I will assume that you mean to ask, "What is the arc length of curve C from t=0 to t=1 if curve C is defined parametrically by x=1+2e^t and y=e^t?"
I can answer this question.
dx/dt=2e^t and dy/dt=e^t.
Arc length = a∫b √[(dx/dt)2+(dy/dt)^2]
= 0∫1 √[4e^(2t)+e^(2t)]dt
= 0∫1 √[5e^(2t)]dt.
= 0∫1 [(√5)(e^t)]dt
= √5 x (e^1-e^0)
= √5 x (e-1)
= e√5-√5.
Difficult? Maybe. Fun? Hopefully. Accurate? Definitely!
Wiki User
∙ 9y ago
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