Evaluate the Differential Is Exact $$\int _ { ( 1,1,1 ) } ^ { ( 2,5,5 ) } \frac { 3 x ^ { 2 } } { y ^ { 3 } } d x - \frac { 3 x ^ { 3 } } { y ^ { 4 } } d y + \frac { 1 } { z } d z$$

question 187

Multiple Choice

Evaluate. The differential is exact.
- $$\int _ { ( 1,1,1 ) } ^ { ( 2,5,5 ) } \frac { 3 x ^ { 2 } } { y ^ { 3 } } d x - \frac { 3 x ^ { 3 } } { y ^ { 4 } } d y + \frac { 1 } { z } d z$$

• A) 0
• B) \(- \frac { 117 } { 125 } + \ln 5\)
• C) \(\frac { 133 } { 125 } + \ln 5\)
• D) \(\frac { 8 } { 125 } + \ln 5\)

---

Definitions:

Charter

A document, especially a legal one, that establishes principles, rights, or privileges in a particular entity, organization, or country.

Mobility Rights

Refers to the rights of individuals to move freely within a country or between countries, often enshrined in law or international agreements.

Charter

A document that establishes a municipality or corporation, outlining its rights, privileges, and purposes.

Revised Statutes

Updated and amended versions of legal codes or laws that have been officially published.