Evaluate By Changing to Spherical Coordinates

question 100

Essay

Evaluate $\int _ { 0 } ^ { 2 } \int _ { - \sqrt { 4 - x ^ { 2 } } } ^ { \sqrt { 4 - x ^ { 2 } } } \int _ { 0 } ^ { \sqrt { 4 - x ^ { 2 } - y ^ { 2 } } } z ^ { 2 } \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } d z d y d x$ by changing to spherical coordinates.

---

Definitions:

Public-Works Projects

Government-funded projects designed to create infrastructure benefiting the public, such as roads, bridges, and schools.

Direct Relief

A form of assistance given directly to needy individuals and families by government or charitable organizations, typically in the form of food, housing, or medical aid.

Industrial Wages

The payment or compensation given to workers in manufacturing, factories, and other sectors within the industrial part of the economy.

Economic Reality

Refers to the actual financial and economic condition of an entity or market, as opposed to what is theorized or planned.