Let $F(x,y)=x^{2}yi+xj,$ and $C$ be the formed by the sides of the triangle with vertices $(0\mathrm{.}0),(1,0),(1,1),$ oriented counterclockwise.

Calculate ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}F*Tds$

a$)$ Without using Green's Theorem, and

b$)$ Using Green's Theorem.