How to prove these with Integral Theorems

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Discussion Overview

The discussion revolves around proving certain challenges posed by a physics lecturer, specifically using Integral Theorems. Participants are seeking guidance on how to approach these problems, which are framed as extra thinking exercises rather than standard homework questions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • Some participants suggest using the divergence theorem as a potential starting point for the proofs.
  • One participant mentions that the first problem can be proved directly and encourages others to visualize the problem by drawing it.
  • A later reply outlines a step-by-step approach, including writing down the divergence theorem and applying it to each problem, while also noting a caution regarding the orientation in one of the problems.

Areas of Agreement / Disagreement

Participants generally agree on the relevance of the divergence theorem, but there is no consensus on the specific methods or steps to take for each problem, leaving the discussion somewhat unresolved.

Contextual Notes

Some assumptions about the problems and their specific requirements are not fully articulated, and there may be dependencies on definitions related to the divergence theorem that are not clarified in the discussion.

Gameowner
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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.
 

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Gameowner said:
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.
 
lavinia said:
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 ><
 
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.
 

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