Use Stoke's Theorem to Evaluate $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$

question 111

Short Answer

Use Stoke's theorem to evaluate $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$ $\mathbf { F } ( x , y , z ) = 6 y x ^ { 2 } \mathbf { i } + 2 x ^ { 3 } \mathbf { j } + 6 x y \mathbf { k }$ C is the curve of intersection of the hyperbolic paraboloid $z = y ^ { 2 } - x ^ { 2 }$ and the cylinder $x ^ { 2 } + y ^ { 2 } = 25$ oriented counterclockwise as viewed from above.

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Definitions:

Tax

A required economic dues or other form of assessment exacted from a taxpayer by government authorities meant to finance government activities and assorted public costs.

Excess Supply

Occurs when the quantity of a good or service supplied is greater than the quantity demanded at a given price.

Supply Function

A mathematical expression representing how the quantity supplied of a good is influenced by its price and possibly other factors.

Demand Function

A mathematical expression that describes the relationship between the quantity of a good demanded and its price.