Find the Center of Mass of a Thin Plate Covering $y = x ^ { 2 }$

question 63

Multiple Choice

Find the center of mass of a thin plate covering the given region with the given density function.
-The region bounded below by the parabola $y = x ^ { 2 }$ and above by the line $y = x + 2$ , with density $\delta ( x ) = 7 x ^ { 2 }$

• A) \(\bar { x } = \frac { 18 } { 5 } , \bar { y } = \frac { 531 } { 70 }\)
• B) \(\bar { x } = \frac { 8 } { 7 } , \bar { y } = \frac { 118 } { 49 }\)
• C) \(\bar { x } = \frac { 531 } { 70 } , \bar { y } = \frac { 18 } { 5 }\)
• D) \(\bar { x } = \frac { 9 } { 8 } , \bar { y } = \frac { 131 } { 64 }\)

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