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

question 29

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 $\int _ { C } \vec { G } \cdot d \vec { r }$

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Definitions:

Supporting Reason

An argument or rationale provided to back up a claim, opinion, or decision.

Peremptory Challenges

The right in jury selection for the prosecution and defense to reject a certain number of potential jurors without stating a reason.

Racial Criteria

Standards or tests based on race, often used in contexts where racial profiling, discrimination or preferential treatment is being examined.

Direct Examination

The initial questioning of a witness during a trial or hearing by the party who called the witness to testify.