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Math Help - Curve Integrals

  1. #1
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    Question Curve Integrals

    "The integral I is defined by

    I=∫F.dr where F(x,y)=(x-y),(xy)

    And C is the triangle with vertices (0,0), (1,0) and (1,3) traversed anticlockwise.

    Calculate the line integral directly"

    I don't know how to get started on this! Please help?
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  2. #2
    MHF Contributor matheagle's Avatar
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    I'd rather use Green's Theorem.
    BUT if you wish to do this directly you need to figure out the three lines parametrically.

    From (0,0) to (1,0)
    you can let y=0, x=t where 0<t<1
    note that dy=0, dx=dt

    From (1,0) to (1,3)
    you can let y=t, x=1 where 0<t<3
    here dy=dt, dx=0

    Finally you have
    (1,3) to (0,0)
    you can let y=3t, x=t BUT 1<t<0 since you are heading to (0,0)
    then dy=3dt, dx=dt
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  3. #3
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    Cool

    The next part of the question is to verify using Green's Theorem. Thanks for that! I knew it involved parametric equations, just wasn't sure on how to set them up.
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