Study guide and 4 practice problems on:

## Ways of computing a line integral

There are several ways to compute a line integral $\int_C \mathbf{F}(x,y) \cdot d\mathbf{r}$:

• Direct parameterization

• Fundamental theorem of line integrals

• Green's theorem

Direct parameterization is the fall-back method. It is convenient when $C$ has a parameterization that simplifies $\mathbf{F}(x,y)$.
The fundamental theorem is usually the easiest to use, but it requires that $\mathbf{F}(x,y)$ is conservative.
Green's theorem only applies when $C$ is closed and $\mathbf{F}$ is well-behaved inside $C$.