1) Suppose that is integrable on for and set . Prove that
2)Compute the value of the improper integral:
.
How to compute and use Fubini and the change of variables formula?
3) Let be a nonempty Jordan region in and be integrable on . Prove that the volume of satisfies
.
Perhaps (2) is the easiest to start with... but I have little idea for (1) and (3)...So thank you for your help.