Find the Average Value Of $f ( x , y ) = x ^ { 2 } + y ^ { 2 }$

question 18

Multiple Choice

Find the average value of $f ( x , y ) = x ^ { 2 } + y ^ { 2 }$ over the region R: square with vertices $( 0,0 ) , ( 2,0 ) , ( 2,2 ) , ( 0,2 )$ .

• A) \(\frac { 8 } { 3 }\)
• B) \(\frac { 32 } { 3 }\)
• C) \(\frac { 16 } { 5 }\)
• D) \(\frac { 4 } { 3 }\)
• E) \(\frac { 8 } { 5 }\)

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