Chapter 6.3, Problem 105E

[T] Evaluate line integral ${\displaystyle \int {}_c\text{F}\text{.d}r,}$

where $F\left(x,y\right)=\left(e^x\sin y-y\right)i+\left(e^x\cos y-x-2\right)j,$ and C is the path given by $r\left(t\right)=\left[t^3\sin \frac{\pi t}{2}\right]i-\left[\frac{\pi }{2}\cos \left(\frac{\pi t}{2}+\frac{\pi }{2}\right)\right]j$ for $0\le t\le 1$

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