Find the Centroid of the Solid Region Bounded by the Graphs

question 41

Multiple Choice

Find the centroid of the solid region bounded by the graphs of the equations. Use a computer algebra system to evaluate the triple integral. (Assume uniform density and find the center of mass.) $$z = \frac { 9 } { y ^ { 2 } + 1 } , z = 0 , x = - 2 , x = 2 , y = 0 , y = 1$$

• A) \(\bar { x } = 2 , \bar { y } = \frac { 2 \ln ( 2 ) } { \pi } , \bar { z } = \frac { 2 + \pi } { 4 \pi }\)
• B) \(\bar { x } = 0 , \bar { y } = \frac { 2 \ln ( 2 ) } { \pi } , \bar { z } = \frac { 9 ( 2 + \pi ) } { 4 \pi }\)
• C) \(\bar { x } = 0 , \bar { y } = \frac { \ln ( 2 ) } { \pi } , \bar { z } = \frac { 9 ( 2 + \pi ) } { 4 \pi }\)
• D) \(\bar { x } = 0 , \bar { y } = \frac { 2 \ln ( 2 ) } { \pi } , \bar { z } = \frac { 9 ( 4 + \pi ) } { 4 \pi }\)
• E)\(\bar { x } = 2 , \bar { y } = \frac { ( 2 + \pi ) 9 } { 4 \pi } , \bar { z } = \frac { 2 \ln ( 2 ) } { \pi }\)

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