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Line Integrals

  1. Dec 4, 2009 #1
    1. The problem statement, all variables and given/known data
    Suppose C is the line segment from the point (1,0) to the point (3,1). Compute the line integral
    intC {( xdx + (x + y)}dy



    2. Relevant equations



    3. The attempt at a solution

    i graphed the line that connects(1,0) to (1,3) and i got the equation of that line
    so y = 1/2(x-1) or y=1/2x -1/2
    dy= 1/2
    i set x=t
    and dx=1
    my endpoints of integration became t=1 and t=3
    then i plugged everything in
    so my integral looked like this
    1<= t<= 3 {(t(1) + (t + (1/2t - 1/2)) }1/2

    i simplified that to this:
    5/4t - 1/4

    and i integrated that over 1->3
    and i got 9/2....but it's wrong?
    can someone tell me what Im doing wrong??
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Dec 4, 2009 #2

    Dick

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    Homework Helper

    I could fuss about your notation a bit but I won't. In {(t(1) + (t + (1/2t - 1/2)) }1/2 you've got the (1/2) from dy multiplying the dx part too. Make it t+(t+(t/2-1/2))*(1/2).
     
  4. Dec 6, 2009 #3
    oh i don't multiply the dy by the whole thing?
    so i seprate the dx from the dy
    but the points of integration at t are still the same tho right?
     
  5. Dec 6, 2009 #4

    Dick

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    Science Advisor
    Homework Helper

    I think you want to integrate x*dx+(x+y)*dy. A line integral (x*dx+(x+y))*dy doesn't make much sense. Everything else seems ok.
     
    Last edited: Dec 6, 2009
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