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Math Help - Determine the Potential Function

  1. #1
    Senior Member bugatti79's Avatar
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    Determine the Potential Function

    Folks,

    Find the potential function for F(x,y)=-2xy^3 \vec i -3x^2y^2 \vec j

    IF we take \phi_x= -2xy^3 and \phi_y=-3x^2 y^2

    Integrating the first one wrt x gives

    \phi (x,y)=\int -2xy^3 dx = -x^2 y^3 +k(y)

    Differentiating the RHS wrt y gives

    -3x^2y^2 +k'(y) but

    \phi_y=-3x^2 y^2 \implies k'(y)=0 \implies k(y)=C

    \phi(x,y)=x^2y^3+C........?

    If I apply  \nabla \phi is end up with the vector field F above.
    Last edited by bugatti79; January 14th 2012 at 10:53 AM. Reason: Found answer
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