Consider a double integral
$$K= \int_{-a}^a \int_{-b}^b \frac{B}{r_1(y,z)r_2^2(y,z)} \sin(kr_1+kr_2) \,dy\,dz$$
where $$r_1 =\sqrt{A^2+y^2+z^2}$$ $$r_2=\sqrt{B^2+(C-y)^2+z^2} $$
I want to maximize $K$ with respect to $ a, b, k, A, B$ and $C$. This involves differentiating K with respect to these variables and then solve the simultaneous equations.
Aside from this method, is there another way to maximize this double integral?