In 29–34 compute … along the straight line … and the parabola…

Find a nonconservative $\mathbf{F}$ whose work around the unit circle $x^2+y^2=1$ is zero.

In 29–34 compute $\int \mathbf{F}\cdot d\mathbf{R}$ along the straight line $\mathbf{R}=t\mathbf{i}+t\mathbf{j}$ and the parabola $\mathbf{R}=t\mathbf{i}+t^2\mathbf{j}$, from $(0,0)$ to $(1,1)$. When $\mathbf{F}$ is a gradient field, use its potential $f(x,y)$.

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §15.2 Line Integrals, #28