Chapter 6.3, Problem 141E

For the following exercises, show that the following vector fields ate conservative by using a computer. Calculate ${\displaystyle \int {}_{c}F.dr}$ for the given curve

141. [T] Let C: [1, 2] $\to$ ${ℝ}^2$be given by $x=e^{t-1},y=\sin \left(\frac{\pi }{t}\right).$ Use a computer to compute the integral ${\displaystyle \int {}_c\text{F}\text{.}ds}={\displaystyle \int {}_{c}2x\cos ydx-x^2\sin ydy,}$where $F=\left(2x\cos y\right)i-\left(x^2\sin y\right)j$ .