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Line integral?

  1. Jan 18, 2009 #1


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    If a question says something like: "evaluate [tex]\int[/tex](x*z*y)dx - (x-y)dy + (x^3)dz from (1,0,0,) to (1,0,2pi) along the curve (x,y,z)=(cos(t),sin(t),t)" or something like that, this is just basically splitting up a line integral? In my example, it would be the same as: [tex]\int[/tex]cos(t)*t*sin(t)) * (-sin(t)) dt - [tex]\int[/tex](cos(t)-sin(t))*cos(t) dt ... etc. , which is just: [tex]\int[/tex]<(cos(t)*t*y),-(cos(t)-y),(cos(t)^3)> dot <-sin(t),cos(t),1> dt from t=0 to t=1 ("dot" represents a dot product).
  2. jcsd
  3. Jan 18, 2009 #2
    Pretty much, though the limits would be from t=0 to t=2pi, and it's the second form of the integral (i.e. the expanded dot product) that is useful to calculate (by evaluating the definite integral with respect to t).
  4. Jan 18, 2009 #3


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    OK, thanks.

    And, er, yeah, I meant from t=0 to t=2pi.
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