Work and Vector Line Integrals

A field pushes a particle along a curve

Two worked computations

Orientation and path language

Other readings of the same integral

To compute the work of $\mathbf{F} = (y, x)$ along $\mathbf{r}(t) = (t, t)$, $0 \le t \le 1$, what is the integrand?

Around the unit circle counterclockwise, which field has circulation $2\pi$?

The circulation of $\mathbf{F}$ around a closed curve counterclockwise is $5$. What is the circulation clockwise?

For $\mathbf{F} = (y, x)$ along the straight path from $(0,0)$ to $(1,1)$, the work is $\int_0^1 2t\, dt$. Give the value, as a plain number.

A field's line integral along a path from A to B is $12$. Give the integral along the reversed path from B to A, as a plain integer like -5.