Engineering Statics

F-24


Determine by direct integration the moment of inertia of the shaded area with respect to the y axis.

Cuts area taken in the y direction, hence, dA = y dx.
A substitution is made for y.  In addition k is found as a function of 
a and b.
Constant are factored out of the integral sign and the integrand is 
simplified.
The integral is performed.
Limits of integration are substituted into the expression.
The moment of inertia about the y axis is found.