Change the Cartesian Integral to an Equivalent Polar Integral, and Then

question 248

Multiple Choice

Change the Cartesian integral to an equivalent polar integral, and then evaluate.
- $\int _ { - 3 } ^ { 3 } \int _ { - \sqrt { 9 - x ^ { 2 } } } ^ { \sqrt { 9 - x ^ { 2 } } } \frac { 1 } { \left( 1 + x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } } d y d x$

• A) \(\frac { 18 } { 5 } \pi\)
• B) \(\frac { 9 } { 5 } \pi\)
• C) \(\frac { 9 } { 19 } \pi\)
• D) \(\frac { 9 } { 10 } \pi\)

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Definitions:

Autonomy

The capacity and freedom to make one's own decisions, often associated with independence and self-determination.

Conscience

An inner feeling or voice viewed as acting as a guide to the rightness or wrongness of one's behavior.

Superego

A component of Sigmund Freud's psychoanalytic theory of personality, which represents the ethical or moral self, holding internalized societal norms and ideals.

Ego

In psychoanalytic theory, the part of the personality responsible for dealing with reality while balancing the demands of the id and superego.