I think you have an extra y in the basic equation - it should be .
Find the moment of inertia of a plate covering the region bounded by x = -1, x = 1, y = 0 and y= 1 with respect to x axis.
Ix = k integral (x^2 * y)
x^2 * 1
so the answer is k * 1/3x^3
and we would plug 1 into x?
the book answer is 2/3k... any hints? thanks.