Question

Evaluate the line integral 2x dx, where C is the line segment from (0, 2) to (2, 6).

Answer 1

You can parametrize C :
\[\vec{r}(t)=(x(t),y(t))=(t, 2t+1) , t\in[0,2]\]
Now we know
\[\int_{c}f\ ds=\int_{a}^{b}f(\vec{r}(t))|\vec{r}(t)|dt\]

Answer 2

Welp meant y(t)=2t+2