Evaluate By Changing to Spherical Coordinates

question 129

Short Answer

Evaluate $\int _ { - 5 } ^ { 5 } \int _ { 0 } ^ { \sqrt { 25 - x ^ { 2 } } } \int _ { 0 } ^ { \sqrt { 25 - x ^ { 2 } - y ^ { 2 } } } \left( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \right) ^ { 1 / 3 } d z d y d x$ by changing to spherical coordinates.

---

Definitions:

Gingivitis

A common and mild form of gum disease (periodontal disease) that causes irritation, redness, and swelling (inflammation) of your gingiva, the part of your gum around the base of your teeth.

Periodontitis

A serious gum infection that damages the soft tissue and destroys the bone supporting teeth, potentially leading to tooth loss.

Mucosa

A moist, inner lining of some organs and body cavities, such as the nose, mouth, lungs, and stomach.

Submucosa

A layer of dense irregular connective tissue or fibrous connective tissue that lies beneath a mucous membrane and supports it, often containing glands, blood vessels, and nerves.