Use Green's Theorem to Evaluate the Line Integral Along the Positively

question 47

Multiple Choice

Use Green's Theorem to evaluate the line integral along the positively oriented closed curve $C$ .
$\oint _ { C } ( 6 x y + 5 \ln ( 1 + x ) ) d x + 2 x ^ { 2 } d y$ , where $C$ is the cardioid $r = 2 + 2 \cos \theta$ .

• A) \(- 20 \pi\)
• B) \(- 80 \pi\)
• C) \(- 10 \pi\)
• D) \(- 40 \pi\)

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Definitions:

Infection

The invasion and multiplication of microorganisms such as bacteria, viruses, and parasites that are not normally present within the body, often causing illness.

Antigen-Presenting Cell

A type of immune cell that displays antigens on its surface, presenting them to T cells, thus initiating an immune response.

Helper T Cell

A type of T cell that plays a crucial role in the immune system by activating and directing other immune cells.

MHC Class II

Major Histocompatibility Complex Class II, a class of molecules found on the surface of immune cells that present antigens to helper T cells, playing a crucial role in the immune response.