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Math Help - Line Integrals

  1. #1
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    Line Integrals

    For F = (4xy - 3(x^2)(z^2))i + (2(x^2))j - (2(x^3)z)k

    (1,0,1) to (1,1,1)

    Show the integral (lower limit c) F.dr is independent of the curve c joining two given points by obtaining a scalar function phi such that F = delta phi. Find the value of the integral between the points given.

    I can find phi

    2(x^2)y - (x^3)(z^2) + c

    But i cant do the integral, what am i integrating? phi?
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  2. #2
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  3. #3
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    That integral is independent of the path because there exist a function
    phi(x,y,z) such that
    d phi= (4xy - 3(x^2)(z^2))dx + (2(x^2))dy - (2(x^3)z)dz
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