I am solving line integrals of vectorial functions and, when the curve along it is defined the integral is given by its parameterization, I have no problem in solving it. However, I am stuck in examples like the following when I need to obtain a parameterization.
The curve is $C=\{(x,y)\in \mathbb{R}^2|x=y^2,y=x^2,0\leq x\leq 1, 0 \leq y \leq 1\}$. Obviously it doesn't work fixing $x=t$ for example. The function to integrate along $C$ is, by the way, $F(x,y)=(2x+y^2,3y-4x)$ Appreciate any kind of help. Thank you.