iriehsu7606 iriehsu7606
  • 12-12-2017
  • Mathematics
contestada

Find the length of the curve. r(t) = cos(2t) i + sin(2t) j + 2 ln(cos(t)) k, 0 ≤ t ≤ π/4

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alekos
alekos alekos
  • 15-12-2017
[tex]dx/dt = -2sin2t: dy/dt = 2cos2t: dz/dt = -2sint/cost[/tex][tex] \int\limits^ \frac{ \pi }{4} _0 { \sqrt{(dx/dt)^2+(dy/dt)^2+(dz/dt)^2} } \, dt [/tex][tex] integral (0 to \pi /4){\sqrt{4sin^22t+4cos^22t+4[tex]int ( \sqrt{4 + 4tan^22t})dt [/tex][tex] \int\ {sect} \, dt ::from::t= 0 to \pi/4 [/tex][tex]ln(sect+tant) from t = 0 to pi/4 [/tex][tex]ln(sec \pi +tan \pi )[/tex][tex]Length = -1[/tex]sin^2t/cos^2t}} dt [/tex]
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