- #1
mill
- 72
- 0
Homework Statement
Calculate the arclength of the curve given parametrically by
##
x=2t^2,
y=\frac 8 5 \sqrt 3t^ \frac 5 2,
z=2t^3
##
for 0≤t≤2
Homework Equations
## S=∫ \sqrt(dx^2 + dy^2 + dz^2) ##
The Attempt at a Solution
1. Found derivative of each and input into equation.
## S=∫\sqrt((4t)^2 + (4\sqrt 3 t^ \frac 3 2 )^2 + (6t^2)^2) dt ##
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+ \frac 3 2 )dt ##
5. Integrated.
##[\frac 2 3 t^3 + \frac 3 2 t^2]##
Which evaluated becomes 34/3. The right answer is 24. I think I have the steps correct. Where did I go wrong?
Last edited: