I've been stuck on this problem for a while now. I have to evaluate the line integral below:
$\int_{C}^{}(x+4 \sqrt{y}) ds \\ C: \vec{r}^{} (t)=t\vec{i}^{} + t\vec{j}^{} \\ 0\leq t \leq 1 $
What I tried to do is:
$ \\x=t, y=t \\ \int_{C}^{}(x+4 \sqrt{y}) ds = \int_{0}^{1}(t+4 \sqrt{t})(\sqrt{(\frac{dx}{dt})^2 + (\frac{dy}{dt})^2} dt= \int_{0}^{1}(t+4 \sqrt{t})(\sqrt{1+1})dt = Undefined $
I don't understand where I've gone wrong in my solution and would greatly appreciate some help.