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Math Help - Urgent: Review problem for Final: Path Independence and Potential Functions

  1. #1
    Member FalconPUNCH!'s Avatar
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    Exclamation Urgent: Review problem for Final: Path Independence and Potential Functions

    This isn't homework but it's on our review for our final and I can't figure out the second part to save my life.

    Question: Let  F(x,y) = (2x + y^{2} + 3x^{2}y)i + (2xy + x^{3} + 3y^{2})j . Show that the line integral  \int_c F*dr is independent of the path, and then find the value of the integral from (0,1) to (5,3).

    The * is supposed to mean dot.

    I know you're supposed to have a F(x) = the i part and F(y) = the j part, take the derivative with respect to x of the i part and take the derivative with respect to y for the j part. I don't know where to go from there.

    thanks
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  2. #2
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    Quote Originally Posted by FalconPUNCH! View Post
    This isn't homework but it's on our review for our final and I can't figure out the second part to save my life.

    Question: Let  F(x,y) = (2x + y^{2} + 3x^{2}y)i + (2xy + x^{3} + 3y^{2})j . Show that the line integral  \int_c F*dr is independent of the path, and then find the value of the integral from (0,1) to (5,3).

    The * is supposed to mean dot.

    I know you're supposed to have a F(x) = the i part and F(y) = the j part, take the derivative with respect to x of the i part and take the derivative with respect to y for the j part. I don't know where to go from there.

    thanks
    Find a scalar function \phi such that F = \nabla \phi:

    \frac{\partial \phi}{\partial x} = 2x + y^2 + 3x^2 y .... (1)


    \frac{\partial \phi}{\partial y} = 2xy + x^3 + 3y^2 .... (2)


    Solve the above simultaneous partial differential equations for \phi.

    The line integral is equal to \phi(5,3) - \phi(0,1).
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