Prove the set is Jordan- measurable and find the appropriate Jordan measure (volume) of the set V.

Question

Prove the set is Jordan- measurable and find the appropriate Jordan measure (volume) of the set V. $$V= \{ (x,y,z)|x^2+y^2\geq 1, x^2+y^2\leq2x, x^2+y^2+z^2 \geq 4, x+y+z\leq 8\} $$

I'm not sure if this question is within the curriculum that we have done thus far, i would appreciate any feedback on solving this.. Can it be solved without integrals ?

Answer 1

This set is not bounded so is not Jordan-mesurable.