# Homework Help: Vector arc length problem

1. Sep 30, 2009

### rwisz

1. The problem statement, all variables and given/known data
Find Arc Length:
r(t)=t^3 i+tj+(1/2)$$\sqrt{6}$$t^2k 1$$\leq$$t$$\leq$$3

2. Relevant equations
The arc length formula:
integrate: sqrt((dx/dt)^2+(dy/dt)^2+(dz/dt)^2) dt

3. The attempt at a solution
I can find the derivative and plug into the formula, it's just the simplification that is absolutely stumping me. I haven't done this for a long time, which is always why my TeX is horribly put together.

Any help is greatly appreciated. I've gotten to here so far:

$$\int_1^3 \! \sqrt{9t^4+1+6t^2} \, dt.$$

2. Sep 30, 2009

### Dick

The expression under the square root is a perfect square. Factor it!

3. Oct 1, 2009

### rwisz

Thank you. I'm sorry for the nonsensical post, I guess I was way too tired to not have that jump out at me.

Again, thank you.