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Line integral

  1. Jan 24, 2014 #1

    etf

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    Here is my task and my attempt of solution:

    line.jpg

    How to use fact that C is positively orientated viewed from point (10,0,0)? I'm not sure I understand it.
     
  2. jcsd
  3. Jan 24, 2014 #2

    LCKurtz

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    It would be much more convenient for us if you would type your question and work on this site instead of posting un-editable images and which require us to open another window.
     
  4. Jan 24, 2014 #3

    LCKurtz

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    Me neither. Perhaps it meant (0,0,10). I would just work it going either direction for ##\theta## and see what happens.
     
  5. Jan 24, 2014 #4

    SammyS

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    Here is the image:
    attachment.php?attachmentid=65981&d=1390608864.jpg

    Is C supposed to be a closed path ?
     
  6. Jan 24, 2014 #5

    LCKurtz

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    It's closed alright. Here's a picture of it:

    curve.jpg
     
  7. Jan 25, 2014 #6

    SammyS

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    Yes the intersection makes a complete loop, but if the instruction is correct regarding the view from (10, 0, 0), then only part of that path is oriented in a positive direction.

    That's why I asked (the OP) if the path is supposed to be closed. If so then the point (10, 0, 0) is incorrect as you have suggested.
     
  8. Jan 25, 2014 #7

    etf

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    I didn't learn latex yet so that's reason why I'm posting images. I could write my equations here but I thought it would be much easier for you to follow if I "draw" it using MathType software.

    It's (10,0,0) point, I didn't make mistake... I'm still uncertain about solving this problem...
    I forgot to write, result is pi.
     
    Last edited: Jan 25, 2014
  9. Jan 25, 2014 #8

    LCKurtz

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    It isn't.

    I think you had best ask your Teacher to clarify. It makes sense to talk about clockwise or counterclockwise orientation if you look down at it along the ##z## axis, but not from out the ##x## axis. And I don't see any interpretation of the problem that gives ##\pi## for the answer. Are you sure you copied the integral itself correctly?
     
  10. Jan 25, 2014 #9

    etf

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    I copied it correctly. I will ask teacher for help.
    Thanks anyway!
     
  11. Jan 25, 2014 #10

    LCKurtz

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    I would be interested to know what your teacher tells you.
     
  12. Jan 25, 2014 #11

    etf

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    I will inform you as soon as he explain me.
     
  13. Jan 25, 2014 #12

    etf

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    Here are few examples with similar statement:

    1.Find [tex]\int\limits_C{} {{y^2}dx + xdy + zdz}[/tex] where C is curve formed by intersection of [tex]{x^2} + {y^2} = x + y[/tex] and [tex]2({x^2} + {y^2}) = z[/tex] orientated positively viewed from point (0,0,2R). (Result 0)

    2.Find [tex]\int\limits_C {(y - z)dx + (z - x)dy + (x - y)} dz\\[/tex] where C is curve formed by intersection of [tex]{x^2} + {y^2} = {a^2}[/tex] and [tex]\frac{x}{a} + \frac{z}{h} = 1[/tex] (a greather than 0, h greather than 0), passed in positive direction viewed from point (2a,0,0). (Result -2*pi*a*(a+h))
     
    Last edited: Jan 25, 2014
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