Calculate the Line Integral Of $\vec{F}=(-9 y+x) \vec{i}+2 x \vec{j}$ Along a Quarter of a Circle Centered at the Origin

question 32

Essay

Calculate the line integral of $\vec{F}=(-9 y+x) \vec{i}+2 x \vec{j}$ along a quarter of a circle centered at the origin, starting at (3, 0)and ending at (0, -3).

---

Definitions:

Cochlear Nerve

A nerve responsible for transmitting auditory information from the cochlea of the inner ear to the brain.

Cochlea

A spiral-shaped, fluid-filled inner ear structure responsible for converting sound waves into nerve impulses.

Basilar Membrane

A membrane in the cochlea of the inner ear that vibrates in response to sound, helping to transmit sound waves to the auditory nerves.

Tympanic Membrane

Also known as the eardrum, it is a thin membrane that separates the external ear from the middle ear and vibrates in response to sound waves.