along parabola \(\displaystyle y=x^{2}\)
\(\displaystyle F(x,y)=2xy^{2}i+2(x^{2}y+y)j\)
Let x=t be the parameter. Then, the path C:
\(\displaystyle x=t, \;\ y=t^{2}, \;\ (0\leq t \leq 2)\)
\(\displaystyle \int_{C}A \cdot dr=\int_{C}\left(2xy^{2}\cdot i+2(x^{2}y+y)j\right)\cdot (dx\cdot i+dy\cdot j)\)
\(\displaystyle =\int_{0}^{2}\left(2t^{5}+2t^{2}(t^{2}+1)(2t)\right)dt\)
