Question

x=20 cos^3(θ) and y=20 sin^3(θ), find the total length of the curve swept out by the point (x,y) as θ ranges from 0 to 2π.

Answer 1

isnt it just ds from 0 to 2pi?

ds = sqrt((x')^2+(y')^2)

Answer 2

http://tutorial.math.lamar.edu/Classes/CalcII/ParaArcLength.aspx

http://tutorial.math.lamar.edu/Classes/CalcII/ParaArcLength_files/eq0008M.gif
^that's what i'd think you need... just dtheta instead of dt.

Answer 3

\[\int_{a}^{b}ds\]
\[\int_{0}^{2\pi}\sqrt{(x')^2+(y')^2}dt\]

Answer 4

Paul does a nice job of explaining things :)