WeBWorK Standalone Renderer

Suppose $\vec{F}(x,y) = \displaystyle 3 \sin\left( \frac{x}{2} \right) \sin\left( \frac{y}{2} \right) \vec{i} - 3 \cos\left( \frac{x}{2} \right) \cos\left( \frac{y}{2} \right) \vec{j}$ and $C$ is the curve from $P$ to $Q$ in the figure. Calculate the line integral of $\vec{F}$ along the curve $C$ .

The labeled points are $P = ( \frac{3\pi}{2},-\frac{3\pi}{2})$ , $Q = ( \frac{3\pi}{2}, \frac{3\pi}{2})$ , $R = (-\frac{3\pi}{2},-\frac{3\pi}{2})$ , and $S = (-\frac{3\pi}{2}, \frac{3\pi}{2})$ . The curves $PR$ and $SQ$ are trigonometric functions of period $2\pi$ and amplitude 1.

$\displaystyle \int_C \vec{F} \cdot d\vec{r}$ =

(Click on graph to enlarge)