Calculating the arc length in r^3

[makman09]

Homework Statement

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

0≤t≤2

Homework Equations

arc length 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))

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.

 

[makman09]

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

 

[voko]

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

 

[HallsofIvy]

Homework Statement

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

0≤t≤2

Homework Equations

arc length 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))

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.

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.

 

[makman09]

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

 

[LCKurtz]

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

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.