How to prove these with Integral Theorems

[Gameowner]

Physics lecturer gave us these as a challenge, and just been thinking and thinking but have no idea as to how to begin, he did hinted that we need to use Integral Theorems, but still not getting anywhere. Anyone else can give me some tips and hints?

these are not homework questions, just extra ''thinking'' problems, so thought this would be a better place to post rather than homework and coursework.

 

[lavinia]

Physics lecturer gave us these as a challenge, and just been thinking and thinking but have no idea as to how to begin, he did hinted that we need to use Integral Theorems, but still not getting anywhere. Anyone else can give me some tips and hints?

these are not homework questions, just extra ''thinking'' problems, so thought this would be a better place to post rather than homework and coursework.

try the divergence theorem

the dirst one can be proved directly pretty easily.

 

[Gameowner]

try the divergence theorem

the dirst one can be proved directly pretty easily.

Would be best to start by drawing the thing? Any chance at all to start me off? I know I'm asking for a bit much here, but I really have no idea ><

 

[zhentil]

Step 1: Write down the divergence theorem.
Step 2: Apply the divergence theorem to each problem.
Step 3: Tell your professor to watch his orientations on problem 2.