Using Green's Theorem, Compute the Counterclockwise Circulation of F Around $\mathrm { F } = ( \mathrm { x } + 2 \mathrm { y } ) \mathbf { i } + ( 9 \mathrm { x } - 6 \mathrm { y } ) \mathbf { j } ; \mathrm { C }$

question 146

Multiple Choice

Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C.
- $\mathrm { F } = ( \mathrm { x } + 2 \mathrm { y } ) \mathbf { i } + ( 9 \mathrm { x } - 6 \mathrm { y } ) \mathbf { j } ; \mathrm { C }$ is the region bounded above by $\mathrm { y } = - 5 \mathrm { x } ^ { 2 } + 28$ and below by $\mathrm { y } = 2 \mathrm { x } ^ { 2 }$ in the first quadrant

• A) \(\frac { 200 } { 3 }\)
• B) \(\frac { 784 } { 3 }\)
• C) \(- \frac { 550 } { 3 }\)
• D) \(- 378\)

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Definitions:

Frequency

The rate at which a vibration occurs that constitutes a wave, either in a material (as in sound waves), or in an electromagnetic field (as in radio waves and light).

Sound Wave

A type of pressure wave generated by vibrating objects, traveling through mediums such as air, water, or solids, and perceived as sound by the human ear.

Müller-Lyer Illusion

A visual illusion in which two lines of the same length appear to be of different lengths because of the orientation of arrow-like tails at their ends.

Depth Cue

Visual information that allows a person to judge the distance or depth of objects in relation to themselves.