Finding the arc length of a parametric curve from 0 to 1

[Mugen Prospec]

Homework Statement

3ti+ 8t$$^{(3/2)}$$j + 12t$$^{2}$$k

0 $$\leq$$ t $$\leq$$ 1

Homework Equations

The Attempt at a Solution

I thought you are supposed to take the derivative of all three then square that. those all go into the length formula

My book says answer should be 15 but I am not doing something right. my test is tomorrow, can some one give me a walk through for this one.

 

[Mark44]

I get 15. For this problem, the quantity under the radical is a perfect square quadratic. Try factoring the quadratic before taking the square root.

 

[Mugen Prospec]

ok I think i got it. thank you