another line integral

[mathstresser]

Evaluate the line integral, where C is the given curve.

\(\displaystyle \L\\\int_{c} zdx+xdy+ydz\)

$\displaystyle C: x=t^2, y=t^3, z=t^2, 0<=t<=1$

I do

\(\displaystyle \L\\\int_{0}^{1}(t^2)(2t) + (t^2)(3t^2) + (t^3)(2t) dt\)

I get 3/2.

Is that the only thing I need to do?

Do I need to do anything with

\(\displaystyle \L\\\sqrt((dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2)\)

???

 

[galactus]

3/2 is the answer.

 

[mathstresser]

thanks