# Calculating the arc length in r^3

1. Aug 14, 2012

### makman09

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

r(t)=ti+2tj+(t^2-3)k or r(t)=(t, 2t, t^2-3)

0≤t≤2

2. Relevant equations

arc lenght formula ∫[the scalar of dr/dt]
I know I can calculate the arc length through the equation above, but the questions asks for
me to utilize this formula.

∫√(t^2+a^2) dt = .5t√(t^2+a^2) + .5a^2 times ln(t+√(t^2+a^2))

3. The attempt at a solution
I couldn't get far on this, but i think it has to do something with another alternative to get the arc length.

If it is difficult reading the problem, i also have a picture of it.

2. Aug 14, 2012

### makman09

Here is the picture of the image
It's #6

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3. Aug 14, 2012

### voko

What is the |dr/dt| in this case?

4. Aug 14, 2012

### HallsofIvy

Staff Emeritus
What, exactly, is your problem? It should be very easy to differentiate that. Have you done that yet? There is no "alternative" needed. Just take the derivative of the vector function, find its length and integrate that.

5. Aug 14, 2012

### makman09

i know right? but the book keeps telling me to use the formula to find the arc length provided with problem number 6.

6. Aug 14, 2012

### LCKurtz

So show us what you get for the integral using the "usual way" and explain why you can't use the given formula. Then we can see what the issue really is for you.