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Line Integral

  • Thread starter joemama69
  • Start date
  • #1
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Homework Statement



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.

Homework Equations





The Attempt at a Solution



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

not sure what to do
 

Answers and Replies

  • #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)?
 
  • #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)=___?
 
  • #4
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f(P) - f(Q) = 5 - 5 = 0
 
  • #5
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is that correct
 
  • #6
dx
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It's correct.
 
  • #7
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If f(x,y,z) = 5, how is grad f not equal to (0,0,0)? Jeez, today's just not my day.
 
  • #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.
 
  • #9
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Oh yeah, duh. I think I need to drink more water or something.
 

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