Let a,b,c \in \mathbb R. Determine:
\displaystyle I = \iiint\limits_{x^2 + y^2 + z^2 \le 1} \cos (ax + by + cz) \mathrm dx \mathrm dy \mathrm dz
Also, show that your result is consistent with the fact the volume of the unit sphere is 4\pi/3.
[originally posted by Noble on TSR]