# Homework Help: Lengths of parametric curves

1. Feb 4, 2012

### bobsmith76

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

x = t^3, y = (3t^2)/2 0<= t <= √3

3. The attempt at a solution

dx/dt = 3t^2
dy/dt = 3t

step 1. √((3t^2)^2 + (3t)^2)

step 2. 3t^2 + 3t

(the book says I can't do that, I don't see why)

step 3. insert √3 into t

Here's the books solution

I understand u substitution but I don't see why it's necessary here. I don't why my method does not follow all the rules.

2. Feb 4, 2012

### vela

Staff Emeritus
Because $\sqrt{a^2+b^2} \ne a+b$. Try it with a=b=1, for instance.

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