889. Find the work of the force field, in each point $(x, y)$ of which the intensity (force acting on a unit mass) $\bar{p}=$ $=(x+y) \bar{i}-x \bar{j}$, when a point mass $m$ describes the circle $x=a \cos t, y=-a \sin t$, moving in the clockwise direction.
Solution. Substituting into formula (5) the projections of the force $\bar{F}=m \vec{p}$ acting on the point: $F_{x}=m(x+y), F_{y}=-m x$, and transforming the curvilinear integral into an ordinary one with variable $t$, we get

$$
\begin{gathered}
E=\oint_{-c} P d x+Q d y=\oint_{-c} m(x+y) d x-m x d y= \\
=\int_{0}^{-2 \pi} m(a \cos t+a \sin t) d(a \cos t)-m a \cos t d(a \sin t)= \\
=-m a^{2} \int_{0}^{-2 \pi}(1+\sin t \cos t) d t=-\left.m a^{2}\left(t+\frac{\sin ^{2} t}{2}\right)\right|_{0} ^{-2 \pi}=2 \pi m a^{2}
\end{gathered}
$$