# Curve integral

1. Nov 1, 2005

### sibiryk

How can I find average distance from the origin point x=y=0 to
the points of the curve using curve integral.

Curve given by

x=cos(2t), y=3sin(2t), t at [0,pi]

I looked in books I have but there is no info on this.

2. Nov 1, 2005

### amcavoy

Find an equation that gives the distance at any value of t. Then integrate it and divide by the interval (def. of average value).

3. Nov 1, 2005

### sibiryk

I need to find it using curve integral

4. Nov 1, 2005

### sibiryk

Ok. I integrated equation that give the distance.

I got

Integral ((cos^2(2t)+6sin^2(2t))^0.5)*dt integral from 0 to pi

Did I get it right?

5. Nov 1, 2005

### NateTG

Close. You need to be more careful with your derivatives and algebra.

6. Nov 1, 2005

### amcavoy

$$3^2\neq 6$$

For this case:

$$\text{Average}=\frac{1}{\pi}\int_{0}^{\pi}f\left(x\right)\,dx$$

Now it's up to you to find f(x).

Last edited: Nov 1, 2005