# Arc length

1. Sep 26, 2014

### Cassi

1. The problem statement, all variables and given/known data

Find the length of the path traced out by a particle moving on a curve according to the given equation during the time interval specified in each case.

The equation is r(t) = a(cos t + t sin t)i + a(sin t - t Cos t)j, 0</=t</=2pi, a>0

2. Relevant equations

Arc length = interval (r'(t)dt)

3. The attempt at a solution

I found the derviative of r(t) to be r'(t) = cost + tsint +atcost +sintt -tcost +atsint
Integrating this from 0->2pi I keep getting 0 because it is subtracting itself. The answer is supposed to be 2pi2a. What am I doing wrong?

2. Sep 26, 2014

### vela

Staff Emeritus
$\vec{r}(t)$ is a vector as is its derivative. You can't simply erase the $\hat{i}$ and $\hat{j}$.

3. Sep 26, 2014

### LCKurtz

And the formula for arc length (integral, not interval) is incorrect. The integrand is $|\vec r'(t)|$.