Solve the Problem Over the Region $0 \leq \mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } \leq 4$

question 119

Multiple Choice

Solve the problem.
-Integrate $\mathrm { f } ( \mathrm { x } , \mathrm { y } ) = \frac { \ln \left( \mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } \right) } { \sqrt { \mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } } }$ over the region $0 \leq \mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } \leq 4$ .

• A) \(4 \pi ( 2 \ln 2\) - 1)
• B) \(4 \pi ( \ln 2\) - 1)
• C) \(8 \pi ( \ln 2 - 1 )\)
• D) \(8 \pi ( 2 \ln 2 - 1 )\)

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