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Line Integral

  1. May 13, 2009 #1
    1. The problem statement, all variables and given/known data

    Let f(x,y,z) be a function of three variables. Suppose that C is an oriented curve lying on the level surface f(x,y,z) = 5. Find the integral grad f dot dr.

    2. Relevant equations



    3. The attempt at a solution

    integral grad f dot dr = integral f(q) - f(p)

    not sure what to do
     
  2. jcsd
  3. May 13, 2009 #2

    dx

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    If a point p is on the level surface f(x,y,z) = 5, what does that tell you about f(p)?
     
  4. May 13, 2009 #3

    gabbagabbahey

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    If the curve you are integrating over lies on the surface f(x,y,z)=5, then surely the endpoints p and q do aswell right?.....So f(p)=___? and f(q)=___?
     
  5. May 13, 2009 #4
    f(P) - f(Q) = 5 - 5 = 0
     
  6. May 14, 2009 #5
    is that correct
     
  7. May 14, 2009 #6

    dx

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    It's correct.
     
  8. May 14, 2009 #7
    If f(x,y,z) = 5, how is grad f not equal to (0,0,0)? Jeez, today's just not my day.
     
  9. May 14, 2009 #8

    dx

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    f(x,y,z) = 5 on the level surface, not everywhere. If it was equal to 5 everywhere, grad f would be zero.
     
  10. May 14, 2009 #9
    Oh yeah, duh. I think I need to drink more water or something.
     
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