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) \(\frac { 8 } { 125 } + \ln 5\)

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Definitions:

Total Area

The sum of all areas in a specified space or surface, often used in geometry and calculus to determine the size or extent of shapes.

Properly Calibrated

Refers to the accurate adjustment of instruments, equipment, or devices to ensure their measurements meet the required standards.

Electronic Control

Systems or devices that use electrical signals to regulate or manage other electronic systems.

Significant Level

This term likely refers to significance level; thus it is the threshold at which the p-value of test results must fall below to reject the null hypothesis, indicating statistical significance.