I have a region given by $$R = |{ax}|+|{by}| \le 1$$ and $$f(x,y) = \iint\limits_{R}{(ax-by)^2 \ \cdot \ (3ab^3+12a^3b-6a^3b^2) \ \cdot \ \sin^2({\pi ax + \pi by}})dxdy$$
I need to find the values of $a$ and $b$ that maximize $f$ and I have no idea where to start.