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Line Integral

  1. Nov 29, 2005 #1
    Find the exact value of http://forums.cramster.com/Answer-Board/Image/cramster-equation-20051129112586326885897811250007777.gif [Broken] where http://forums.cramster.com/Answer-Board/Image/cramster-equation-20051129110356326885883583125005816.gif [Broken] and C is the line segment from (1,2,1) to (6,4,5).
    i, j, k are unit vectors
    So far all i have done is drawn in the line segment on a 3D graph.. Look at the URLS for the integral and the F(x,y,z)
     
    Last edited by a moderator: May 2, 2017
  2. jcsd
  3. Nov 29, 2005 #2
    [tex]\int_C\mathbf{F}\cdot d\mathbf{r}[/tex]

    [tex]\mathbf{F}=\left<x^4e^y,\,\ln{z},\,\sqrt{y^2+z^2}\right>[/tex]

    [tex]\mathbf{r}=\left<1+5t,\,2+2t,\,1+4t\right>;\quad 0\leq t \leq 1[/tex]

    Can you figure it out from here?
     
    Last edited by a moderator: May 2, 2017
  4. Nov 29, 2005 #3
    OK i worked off of what you got and i got
    http://www.freemathhelp.com/forum/mimetex/pictures/d1183703930c2d1a7c5a37255ca42e49.gif [Broken]
    But this integral looks VERY hard to solve
     
    Last edited by a moderator: May 2, 2017
  5. Nov 30, 2005 #4

    arildno

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    A few hints:
    For the first term, use integration-by-parts, and for the third term, complete the square in the form: [itex]K\sqrt{(t+a)^{2}+b}[/itex], where K,a,b are appropriate constants. Dependent upon the sign of b, we may write [itex]b=\pm{c}^{2}[/itex] where c is some constant.

    See if you manage to make the last few steps on your own..
     
    Last edited by a moderator: May 2, 2017
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