Use Stoke's Theorem to Evaluate $C$ Is the Curve of Intersection of the Hyperbolic Paraboloid

question 81

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.

---

Definitions:

Antedated

Refers to a document or event dated earlier than the actual date, often done to give the appearance of an earlier occurrence.

Material Fact

A fact that is significant or essential to the issue or matter at hand, which, if known, could influence an individual's decision.

Nondisclosure

An agreement or clause that prohibits the sharing of confidential information.

Material Fact

Information that is significant enough to influence a decision or the outcome of a legal case or transaction.