Arc Length

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



Calculate the arclength of the curve given parametrically by



x=2t^2

y=(8/5)sqrt(3)t^(5/2)

z=2t^3



for 0≤t≤2



2. Relevant equations



S=∫sqrt(x'^2 + y'^2 + z'^2)



3. The attempt at a solution



1. Found derivative of each and input into equation.

2. S=∫sqrt(16t^2 + 48t^3 + 36t^4)dt

3. S=∫2t sqrt(4 + 12t + 9t^2)dt

4. Used complete the square



=∫2t (t+ (3/2))dt



5. Integrated.

[(2/3)t^3 + (3/2)^t^2]



Which evaluated becomes 34/3. The right answer is 24. Where did I go wrong?