Solution
= Solution
Contract the isotropic expression from (i). Since $\delta_{ii}=3$ and $\delta_{ij}\delta_{ij}=3$,
$$
I_{iijj}=A(9+3+3)=15A.
$$
The value in (ii) gives $A=4\pi/105$, so the <isotropic fourth moment of a ball> is
$$
\boxed{I_{ijkl}=\frac{4\pi}{105}(\delta_{ij}\delta_{kl}+\delta_{ik}\delta_{jl}+\delta_{il}\delta_{jk}).}
$$
For example $\int_Bx_1^4\,dV=4\pi/35$ and $\int_Bx_1^2x_2^2\,dV=4\pi/105$, illustrating the factor of three between these two fourth moments.