Find the exact length of the parametric curve 0<t<pix = cos*e^ty= sin *e^t

Kye 2020-10-18 Answered

Find the exact length of the parametric curve 0<t<π
x=coset
y=sinet

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Expert Answer

Laith Petty
Answered 2020-10-19 Author has 103 answers

Let y=f(x), axby=f(x),axb be the given curve.The arc length L of such curve is given by the definite integral
L=ab1+[f(x))2dx
Let x=g(t), y=h(t) where cxdcxd be the parametric equations of the curve y=f(x).
Then the arc length of the curve is given by
L=cd(dxdt)2+(dydt)2dt
Here x(t)=coset,y(t)=sinet where 0<t<π be the parametric equations of the curve y=f(x). Then the arc length of the curve is given by
L=0πsqt((sinet)2+(coset)2dt)
=0πsqt(sin2et+cos2etdt)
=0πdt
=π

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