Solution
= Solution
{c}
For a continuous <vector field> along an oriented piecewise continuously differentiable <parametric curve> $\gamma:[a,b]\to\mathbb R^3$, define its <line integral> by
$$
\boxed{\int_C\mathbf F\cdot d\mathbf r=\int_a^b\mathbf F(\gamma(t))\cdot\gamma'(t)\,dt,}
$$
adding the integrals over the smooth pieces when necessary. The value refers to the specified traversal: going around a curve twice counts twice.