My question is concerned with the parameterisation of a straight line such that I can solve a line integral of the form:
$$\int_c \mathbf F\cdot d\mathbf r$$
where C is the straight line segment from $(0, 0)$ to $(1, 4)$ and $F = [ y^2, -x^2]$.
$$\int_c \mathbf F\cdot d\mathbf r = \int_a^b \mathbf F\cdot \mathbf r'(t)dt$$ where $a = t_1, b = t_2$
would be the way to solve the problem. But how do I parameterise C, $y = 4x$, in the form $\mathbf r(t) = [?, ?]$ so that I can actually do the calculus?