Chapter 7.6, Problem 51E

a)

To determine

To graph: The region restricted by the equations $y=x^2,y=b$, where $b>0$

(b)

To determine

To calculate: The moment around $y$-axis, $M_y$ and $\overline{x}$ of equations $y=x^2,y=b$. Where $b>0$

(c)

To determine

If $\overline{y}>\frac{b}{2}\text{ or }\overline{y}<\frac{b}{2}$ for the equations $y=x^2,y=b$. Where $b>0$

d)

To determine

To prove: The $\overline{y}$ coordinate of centroid of region is more than $\frac{b}{2}$ for $y=x^2,y=b$