The question reads: Evaluate $$ \int_\gamma f(z)dz$$ where $$f(z)=x^2: x,y \in \mathbb{R} $$ and $\gamma$ is the parabola $y=2x^2$ from $x=0$ to $x=2$.
This is the first question I've encountered where $f(z)$ is given in the form $u(x,y)$, and I've been lost as to how I should go about solving it. I started by parameterizing the parabola as $\gamma(t)=t+i2t^2$ but I can't see what to do from here. Any tips will be greatly appreciated, thanks!.