Use Green's Theorem And/or a Computer Algebra System to Evaluate $\int _ { C } x ^ { 2 } y d x - x y ^ { 2 } d y$

question 19

Multiple Choice

Use Green's Theorem and/or a computer algebra system to evaluate $\int _ { C } x ^ { 2 } y d x - x y ^ { 2 } d y$ , where $C$ is the circle $x ^ { 2 } + y ^ { 2 } = 64$ with counterclockwise orientation.

• A) \(8 \pi\)
• B) \(64 \pi\)
• C) \(2 \pi\)
• D) \(- 32 \pi\)
• E) None of these

---

Definitions:

Informational Influence

A form of social influence involving the change in beliefs or behavior that occurs when an individual accepts information from others as evidence about reality.

Group Norms

Accepted standards or behaviors shared by a group's members, guiding their actions and decisions.

Injunctive Norm

A type of social norm that describes what is commonly approved or disapproved within a culture or group.

Normative Influence

The influence of other people that leads us to conform in order to be liked and accepted by them, often resulting in public compliance but not necessarily private acceptance.