Chapter 16.2, Problem 29E

(a) Evaluate the line integral ${\displaystyle \underset{C}{\int }F\cdot dr}$, where $F\left(x,y\right)=e^{x-1}i+xyj$ and C is given by $r\left(t\right)=t^{2}i+t^{3}j,0\le t\le 1$.

(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).