Chapter 9, Problem 14P

The cross section of an airfoil is described by the shaded area that is bounded by a cubic equation $y\left(x\right)=-x^3+9x$, as shown in Fig. P9.14.

1. Given the above equation for $y\left(x\right)$, determine the height h and width b of the fin.
2. Determine the area of the cooling of the fin by integration with respect to $x$.
3. Determine the x-coordinate of the centroid by integration with respect to $x$.
4. Determine the y-coordinate of the centroid by integration with respect to $x$.