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Evaluate the Integral R(x2+y2)2dA\int _ { R } \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } d A

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Evaluate the integral R(x2+y2)2dA\int _ { R } \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } d A , where R is the region shown below.  Evaluate the integral  \int _ { R } \left( x ^ { 2 } + y ^ { 2 } \right) ^ { 2 } d A  , where R is the region shown below.


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