Find Length of Curve x=cos(2t), y=3sin(2t): 0 or Not?

[sibiryk]

I need to find length of the curve x=cos(2t), y=3sin(2t), t[0,p]

I'm getting a length of this curve to be equal zero.
I think it is because this curve is closed and start point = end point.
Is it normal?
How can I get a length of this curve?

 

[whozum]

No you should still be getting a length, what procedure are you using? Show the integral you set up.

 

[mathmike]

length of a arc is given by

s = # * r

# is the internal angle in rads

r is radias

 

[sibiryk]

I got

s(t)=Integral (2sin(2t)-6cos(2t))dt

integral from 0 to pi

 

[whozum]

I remember the arc length integral being more complex than that.. can you explain how you set it up/

 

[TD]

The length of a curve f given in parametric form can be calculated with

\int_a^b {\left\| {\frac{{d\vec f}}{{dt}}} \right\|dt}

Which is, written out in 2 variables:

\int_a^b {\sqrt {x'\left( t \right)^2 + y'\left( t \right)^2 } dt}

 

[Benny]

A tip: \sqrt {x^2 } = \left| x \right| \ne x,\left| x \right| = x \Leftrightarrow x \ge 0