# Length of the curve

1. Oct 31, 2005

### 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?

2. Oct 31, 2005

### whozum

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

3. Oct 31, 2005

### mathmike

length of a arc is given by

s = # * r

# is the internal angle in rads

4. Oct 31, 2005

### sibiryk

I got

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

integral from 0 to pi

5. Oct 31, 2005

### whozum

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

6. Oct 31, 2005

### 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:

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

7. Nov 1, 2005

### Benny

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