Using Green's Theorem, Calculate the Area of the Indicated Region $\mathbf { r } ( \mathrm { t } ) = ( 11 \cos \mathrm { t } ) \mathbf { i } + ( 11 \sin \mathrm { t } ) \mathbf { j } , 0 \leq \mathrm { t } \leq 2 \pi$

question 42

Multiple Choice

Using Green's Theorem, calculate the area of the indicated region.
-The circle $\mathbf { r } ( \mathrm { t } ) = ( 11 \cos \mathrm { t } ) \mathbf { i } + ( 11 \sin \mathrm { t } ) \mathbf { j } , 0 \leq \mathrm { t } \leq 2 \pi$

• A) \(121 \pi\)
• B) \(2 \pi\)
• C) \(11 \pi\)
• D) \(22 \pi\)

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Definitions:

Ciliated

Relating to or having tiny hair-like structures on the surface that move in a wavelike manner to propel substances.

Smooth Muscle

A type of muscle found in the walls of internal organs and blood vessels, functioning involuntarily to regulate bodily processes.

Bronchioles

Small airways in the lungs that branch off from the bronchi, leading to the alveoli where gas exchange occurs.

Ciliary Action

The movement of cilia, small hair-like structures, to move particles or fluid over their surface, commonly seen in respiratory and reproductive tracts.