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

question 416

Multiple Choice

Change the Cartesian integral to an equivalent polar integral, and then evaluate.
- $$\int _ { 0 } ^ { \ln 4 } \int _ { 0 } ^ { \sqrt { ( \ln 4 ) ^ { 2 } - y ^ { 2 } } } e \sqrt { x ^ { 2 } + y ^ { 2 } } d x d y$$

• A) \(\frac { \pi ( 4 \ln 4 + 3 ) } { 2 }\)
• B) \(\frac { \pi ( 4 \ln 4 + 3 ) } { 4 }\)
• C) \(\frac { \pi ( 4 \ln 4 - 3 ) } { 4 }\)
• D) \(\frac { \pi ( 4 \ln 4 - 3 ) } { 2 }\)

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Definitions:

Territory

An area that an animal or group of animals consistently defends against conspecifics or sometimes predators, often for resources or mating rights.

Economic Defensibility

The concept in socioecology that a resource can be defended against competitors at a cost that is less than or equal to its value.

Arbitrary Contest Resolution

A method of determining the outcome of a conflict among animals or individuals using signals or behaviors that do not directly relate to the physical strength or dominance of the participants.

Resource-Holding Potential

The ability of an organism to defend resources such as food, territory, or mates against competitors, which can affect its reproductive success.