Let $\bar { x }$ denote the x-coordinate of the centroid of the region enclosed by $y = 1 - x ^ { 2 }$ and $y = 0$ Then $\bar { x }$ =

A)1
B) $\frac { 1 } { 3 }$
C) $\frac { 93 } { 35 }$
D) $\frac { 3 } { 4 }$
E)0

Question

Let $\bar { x }$ denote the x-coordinate of the centroid of the region enclosed by $y = 1 - x ^ { 2 }$ and $y = 0$ Then $\bar { x }$ =

A)1
B) $\frac { 1 } { 3 }$
C) $\frac { 93 } { 35 }$
D) $\frac { 3 } { 4 }$
E)0

Quizplus · Accepted Answer

The centroid $\bar{x}$ of a symmetric region about the y-axis is always 0 because the region's area on the left of the y-axis is exactly balanced by the area on the right. The given parabola $y = 1 - x^2$ is symmetric about the y-axis, so $\bar{x} = 0$.

Let xˉ\bar { x }xˉ Denote the X-Coordinate of the Centroid of the Region Enclosed

Let $\bar { x }$ Denote the X-Coordinate of the Centroid of the Region Enclosed