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Line Integrals

  1. Apr 29, 2005 #1
    Greetings All,

    I need serious help with this problem , well maybe several problems but I'll take it one at a time:

    Compute the line integral of (4xz + 2y)dx where C is the line segment from (2,1,0) to (4,0,2).

  2. jcsd
  3. Apr 29, 2005 #2
    [tex] \int_c f(x,y,z) ds = \int_a^b f(x(t), y(t), z(t)) \sqrt { \left( \frac{dx}{dt} \right)^2 + \left( \frac{dy}{dt} \right)^2 + \left( \frac{dz}{dt} \right)^2 } [/tex]

    so, you need to parametricize your line in space. par exemple:

    [tex] \begin{align*}
    x=2 + 2t \\
    y=1 - t \\
    z=2t \\

    those are *supposed* to be "less than or equal to" signs, but i never was able to find those.....

    anyhow, you ought to be set to solve this puppy, unless you made it to here and collapsed....
    Last edited: Apr 29, 2005
  4. Apr 29, 2005 #3
    Well, he didn't have any annoying [itex]ds[/itex] to deal with.

    All he needs to do is parameterize the curve and plug in for x, y, z, dx.
  5. Apr 29, 2005 #4
    oh, indeed, it is a dx. ecks, ess, they sound so similar in my noisy head...
  6. Apr 29, 2005 #5
    What a strange problem.
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