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Math Help - Integral and vector fields

  1. #1
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    Integral and vector fields

    Hi,

    having a problem with this one:

    F is a vector field in R3 : F(x,y,z)=(yz,xz,xy)
    \gamma is a curve : (x(t),y(t),z(t))=(cos t, sin t, t), 0<= t <= pi/4

    find the integral of F over \gamma by using the curve's parameters.

    if anybody can help me, thank you!
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  2. #2
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    Standard curve integral:

    where
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  3. #3
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    I believe what you're looking for is

    \int_C {\bf F}\cdot {\bf dr} = \int_C yz dx + xzdy + xydz

    As the vector field is conservative then (the potential \phi = xyz) then the integral is

     \int_C yz dx + xzdy + xydz = \left. xyz \right|_{p_1}^{p_2} where p_1 and p_2 are the starting and finishing points.
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