Use Stokes' Theorem to Evaluate $\oint _ { C } \mathbf { F } \cdot d \mathbf { r }$

question 41

Multiple Choice

Use Stokes' Theorem to evaluate $\oint _ { C } \mathbf { F } \cdot d \mathbf { r }$ . $\mathbf { F } ( x , y , z ) = 7 \cos x \mathbf { i } + 5 e ^ { y } \mathbf { j } + 2 x y \mathbf { k }$ ; C is the curve obtained by intersecting the cylinder $x ^ { 2 } + y ^ { 2 } = 1$ with the hyperbolic paraboloid $z = x ^ { 2 } - y ^ { 2 }$ , oriented in a counterclockwise direction when viewed from above

• A) \(- 2 \pi\)
• B) 0
• C) \(\pi\)
• D) \(1\)

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Definitions:

Bladder

An organ that stores urine produced by the kidneys before it is excreted from the body.

Filtration

A process that separates solids from liquids or gases using a filter medium that allows only the fluid to pass through.

Nephron

The primary unit within the kidney that serves to filter blood and create urine, functioning as both a structural and operational entity.

Trigone

The triangular area located in the urinary bladder base, pivotal in bladder functionality and voiding.