Math Help - Integral-weird

1. Integral-weird

1. Evaluate the differential form $ydx + zdy + xdz$ on the following line segment: $(0,2,-1)$ to $(3,0,1)$.

So $\begin{cases} x = 3t \\ y = 2-2t \ \ \ \ \ \ 0 \leq t \leq 1 \\ z = 2t-1 \end{cases}$ so that $dx = 3dt, \ \ dy = -2dt, \ \ dz = 2dt$.

Then $\int_{(0,2,-1)}^{(3,0,1)} ydx + zdy + xdz = \int_{0}^{1} (2-2t)(3dt) + (2t-1)(-2dt) + (3t)(2dt)$

Is this correct?

2. Yes, that appears to be correct.

I get 6 as the value. Is that what you get?.

3. yeah thats what I got.

Thanks