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Homework Help: Need help with these 3 integrals problems

  1. Apr 5, 2007 #1
    URGENT !!! need help with these 3 integrals problems

    Hi, I need urgent help with these 3 integrals problems ... been stuck on the questions and the deadline is Friday. Thanks a lot ! :smile:

    1) For the green's theorem,
    >> see attach

    I got the answer : 27.552. Not sure whether it is correct. Please kindly explain in steps so I know where I went wrong.


    2) I'm totally unsure about finding the surface integral. How do I know the shape of the surface ?
    >> see attach


    3) and finding the curl function f
    >> see attach

    All I know is, it has something to do with curl. Something like F = grad f. How do I find the function ?


    Thanks again ! :smile:
     

    Attached Files:

  2. jcsd
  3. Apr 5, 2007 #2

    cristo

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    You need to show your work before we can help you. For 1. a numerical answer will not help us see where/if you've gone wrong!
     
  4. Apr 6, 2007 #3

    HallsofIvy

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    No, it is not correct. I don't know what to tell you since you say nothing about what you attempted.


    ?? Because you are TOLD the shape of the surface? What shape in x2+ y2= a2? Remember that this is in 3 dimensions. Since there is no "z" in that equation, what are the possible values for z for each (x,y)?


    The problem says specifically "Find f such that grad f= F". That has nothing to do with the curl. Are you given a specific function F? How you would do this (or even whether it is possible) depends heavily on the form of F. Notice that F has to be vector valued function and f a scalar valued function.

    Please show your work and we may be able to give you some hints.
     
  5. Apr 6, 2007 #4
    Hi, thanks for reply. For 2), the shape should be cylinder with radius a. I think the parametric eqn is, acos@i + asin@j + zk, 0<= @ <= 2pi, 0<= z <= h. for ru x rv = -(acos@)i - (asin@)j + (acos^2@ + asin^2@)k. Is it correct ? I need to know how to find out how to derive the magnitude and evaluate the integral. Any idea ? Thanks.

    I'm still working on 3). Thanks for checking the ans for 2), I guess my working is correct.
     
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