Problem B $(50$ points$)$

Using analytical integration, determine the rectangular moments of inertia and the radii of

gyration of the shaded area below with respect to the indicated x and y axes. The shaded area is

bounded by the curves y$=2$asin$($bx$)$ and y$=$asin$(2$bx$)$ over the range xpi $,$ with a$=$

$1$cm$,$b$=1$radia$($n$)/($c$)$m$,$ and x and y measured in centimeters.