Change the Cartesian Integral to an Equivalent Polar Integral, and Then

question 45

Multiple Choice

Change the Cartesian integral to an equivalent polar integral, and then evaluate.
- $\int _ { - 9 } ^ { 0 } \int _ { - \sqrt { 81 - x ^ { 2 } } } ^ { 0 } \frac { 1 } { 1 + \sqrt { x ^ { 2 } + y ^ { 2 } } } d y d x$

• A) \(\frac { \pi ( 9 + \ln 10 ) } { 2 }\)
• B) \(\frac { \pi ( 9 + \ln 10 ) } { 4 }\)
• C) \(\frac { \pi ( 9 - \ln 10 ) } { 4 }\)
• D) \(\frac { \pi ( 9 - \ln 10 ) } { 2 }\)

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Definitions:

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The value of the next best alternative foregone as a result of making a decision.

Special Order

A customer request for a product or service that is not generally available or outside the business’s normal operations, often requiring special pricing or production considerations.

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The maximum level of output that a company can sustain to make a product or provide a service under normal conditions.

Activity-Based System

A method in accounting that allocates costs to specific activities based on their use of resources, aimed at providing more accurate cost information.