Use Stokes' Theorem to Calculate the Circulation of the Field $\mathbf { F } = 2 \mathrm { y } \mathbf { i } + 8 x \mathbf { j } + \mathrm { z } ^ { 3 } \mathbf { k } ; \mathrm { C } :$

question 109

Multiple Choice

Use Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated direction.
- $\mathbf { F } = 2 \mathrm { y } \mathbf { i } + 8 x \mathbf { j } + \mathrm { z } ^ { 3 } \mathbf { k } ; \mathrm { C } :$ the counterclockwise path around the perimeter of the triangle in the $x - y$ plane formed from the $x$ -axis, $y$ -axis, and the line $y = 5 - 4 x$

• A) \(\frac { 75 } { 2 }\)
• B) \(\frac { 15 } { 4 }\)
• C) \(- \frac { 75 } { 2 }\)
• D) \(\frac { 75 } { 4 }\)

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Definitions:

B Cells

A type of white blood cell that plays a key role in the body's immune response by producing antibodies.

Monocytes

A type of white blood cell that plays a key role in the immune system by removing pathogens and dead or damaged cells from the blood.

Helper T Cells

A type of T cell that plays a crucial role in the immune system by assisting other cells in recognizing and fighting off infections.

Antibody-mediated Response

The antibody-mediated response is an immune response where B cells produce specific antibodies targeting and neutralizing pathogens, a key aspect of the body's adaptive immunity.