(a) Verify Green's theorem in the xy-plane for $\oint_C (2xy - x^2) d…

Question

(a) Verify Green's theorem in the xy-plane for $\oint_C (2xy - x^2) dx + (x^2 + y^2) dy$ where $C$ is the boundary of the region enclosed by curves $y = x^2$ and $x = y^2$.

(b) Evaluate $\oint_C \vec{F} \cdot d\vec{r}$ around a triangle in the xy-plane with vertices at $(0, 0)$, $(3, 0)$ and $(3, 2)$ taken in counter clockwise direction, where $\vec{F} = (2x - y + 4)\hat{i} + (5y + 3x - 6)\hat{j}$.

Related pages

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