Let C Be the Circular Path Which Is the Portion $\vec { G } = x ^ { 6 } y ^ { 3 } \vec { i } + \left( x ^ { 3 } y ^ { 6 } + 6 x \right) \vec { j }$

Essay

Let C be the circular path which is the portion of the circle of radius 1 centered at the origin starting at (1, 0)and ending at (0,-1), oriented counterclockwise.
Let $\vec { G } = x ^ { 6 } y ^ { 3 } \vec { i } + \left( x ^ { 3 } y ^ { 6 } + 6 x \right) \vec { j }$ Determine the exact value of $\int _ { C } \vec { G } \cdot d \vec { r }$