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(a) Evaluate the line integral $\int_{c} \mathbf{F} \cdot d \mathbf{r},$ where

$\mathbf{F}(x, y)=e^{x-1} \mathbf{i}+x y \mathbf{j}$ and $C$ is given by

$\mathbf{r}(t)=t^{2} \mathbf{i}+t^{3} \mathbf{j}, 0 \leqslant t \leqslant 1$

(b) Illustrate part (a) by using a graphing calculator or computer to graph $C$ and the vectors from the vector field corresponding to $t=0,1 / \sqrt{2},$ and 1 (as in Figure 13$)$ .

a) $\int_{C} \mathbf{F} \cdot d \mathbf{r}=\frac{11}{8}-\frac{1}{e}$

b) see graph for answer

Vector Calculus

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