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) $\bar { x } = \frac { 9 } { 8 } , \bar { y } = \frac { 131 } { 64 }$

Question

Quizplus · Accepted Answer

The center of mass $(\bar{x}, \bar{y})$ is calculated using the formulas for a region with variable density. The limits of integration are determined by the intersection points of the parabola and the line, which are $x = -1$ and $x = 2$. The correct calculations yield $\bar{x} = \frac{8}{7}$ and $\bar{y} = \frac{118}{49}$.

Find the Center of Mass of a Thin Plate Covering y=x2y = x ^ { 2 }y=x2

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