Find The Exact Length Of The Curve: x= Et +...

iBrain

From: US
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Find the exact length of the curve: x= et + e-t and y= 5-2t between 0 < t< 3 Thanks again for the help!!

 

Answer No.1

Anonymous

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1. Arclength = Integral of sqrt( (dx/dt)^2 + (dy/dt)^2 ) from0 to 3 2. dx/dt = exp(t) - exp(-t) and dy/dt = -2 3. Integral from 0 to 3 of sqrt((exp(t) -exp(-t) )^2 + 4) = Integral sqrt( exp(2t) + 2 +exp(-2t)) = Integral exp(t)+exp(-t) = exp(t) - exp(-t) 4. Evaluating the above yields exp(3) - exp(-3)

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