Evaluate the Iterated Integral by Converting to Polar Coordinates $\int _ { - 3 } ^ { 3 } \int _ { 0 } ^ { \sqrt { 9 - y ^ { 2 } } } \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 3 / 2 } d x d y$

question 92

Multiple Choice

Evaluate the iterated integral by converting to polar coordinates. Round the answer to two decimal places. $\int _ { - 3 } ^ { 3 } \int _ { 0 } ^ { \sqrt { 9 - y ^ { 2 } } } \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 3 / 2 } d x d y$ .

• A) \(152.68\)
• B) \(5.65\)
• C) \(14.14\)
• D) \(48.6\)
• E) \(381.7\)

---

Definitions:

Common Bond

The shared connection or mutual interest that ties members of a group or community together.

Common Identity

A form of social identity that emphasizes unity and shared characteristics among members of a group, fostering a sense of belonging.

Communal Sharing

A relational model theorizing how people in a group share resources and responsibilities without keeping track of individual contributions or distributions.

Entitativity

The perception or degree to which a group of entities is considered to be a coherent, single unit.