Unsolved Textbook Exercises: Seeking Help and Solutions

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The discussion centers around a user seeking help with unsolved textbook exercises, particularly in vector calculus and integrals, in preparation for an upcoming test. Key issues include confusion over the application of gradient and divergence, as well as difficulties in understanding specific problems related to Stokes' theorem and surface integrals. Participants emphasize the importance of showing work and understanding concepts rather than just receiving answers. The conversation includes detailed explanations of mathematical concepts, with users gradually clarifying their misunderstandings. Overall, the thread highlights a collaborative effort to solve complex mathematical problems and improve comprehension.
  • #51
Post in detail how you get the answer in 6)
 
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  • #52
i got 4 for z=0 to z=2 for (z^2-1) then integrate get 2pie x r since r=2 then 4 times 4pie get 16pie
 
  • #53
Ok, you've got two disks you've got to integrate over in 6)

a) The disk placed at z=2.
At that plane, we have :
\vec{F}\cdot\vec{n}=(z^{2}-1)|_{(z=2)}=3
Or, it's contribution is: 3*\pi(2)^{2}=12\pi

b) The disk placed at z=0
At that plane, we have:
\vec{F}\cdot\vec{n}=(1-z^{2})|_{(z=0)}=1
Or, it's contribution is: \pi(2)^{2}=4\pi

Is this how you thought?
 
  • #54
ya... i did it like that
 
  • #55
i had been doing these qs over the past few weeks and there are still some questions remained unsolved.. anyone can help ?
q3, 7, 8, 9, 13, 14, 15
 
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