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Arc Length for Parametric Equations
L = ∫βα √ ((dx/dt)2 + (dy/dt)2) dt
Note: that we could have utilized the second formula for ds above is we had supposed instead that
dy/dt > 0 for α < t < β
If we had moved out this route in the derivation we would have gotten similar formula.
examples of plane figures
1. A direction ?eld for a differential equation is shown. Draw, with a ruler, the graphs of the Euler approximations to the solution curve that passes through the origin. Use step
L.H.S. =cos 12+cos 60+cos 84 =cos 12+(cos 84+cos 60) =cos 12+2.cos 72 . cos 12 =(1+2sin 18)cos 12 =(1+2.(√5 -1)/4)cos 12 =(1+.(√5 -1)/2)cos 12 =(√5 +1)/2.cos 12 R.H.S =c
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