Work by line integrals

The work done is given by the line integral:

$\displaystyle \int_C \overrightarrow{F} \cdot d \overrightarrow{r}$ = $\displaystyle \int_C \overrightarrow{F}(\overrightarrow{r}(t)) \cdot \overrightarrow{r}\prime(t) dt$

$\displaystyle \overrightarrow{F}(\overrightarrow{r}(t)) = <\cos^2(t),\sin(t) \cos(t)>$

$\displaystyle \overrightarrow{r\prime}(t)=<-\sin(t),\cos(t)>$

Therefore the work done is:

$\displaystyle \int_{0}^{\pi/2} (-2\cos^2(t)\sin(t))dt$

= $\displaystyle \frac{-2}{3}$