Problem 27 **/***

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]

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Pretty sure I was at my oxford interviews with Noble