Let (mathbf{r}(t)=leftlangle t^{2}(1-t), t(t-1)^{2}ightangle). (a) GU Plot the path (mathbf{r}(t)) for (0 leq t leq 1). (b)

Question:

Let $\mathbf{r}(t)=\left\langle t^{2}(1-t), t(t-1)^{2}ightangle$.

(a) GU Plot the path $\mathbf{r}(t)$ for $0 \leq t \leq 1$.

(b) Calculate the area $A$ of the region enclosed by $\mathbf{r}(t)$ for $0 \leq t \leq 1$ using the formula $A=\frac{1}{2} \oint_{C}(x d y-y d x)$.