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SlideMan
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Homework Statement
I need to determine the potential of the following function:
[tex]F = [2x(y^3 - z^3), 3x^2y^2, -3x^2z^2][/tex]
The equation is given to be independent of path, and [tex]F \cdot dr = 0[/tex]
The Attempt at a Solution
[tex]\frac{\partial f}{\partial x} = 2xy^3 - 2xz^3 \Rightarrow f(x,y,z) = x^2y^3 - x^2z^3 + g(y,z)[/tex]
[tex]\frac{\partial f}{\partial y} = 3x^2y^2 = 3x^2y^2 + \frac{\partial g}{\partial y} \Rightarrow g(y,z) = h(z)[/tex]
[tex]\frac{\partial f}{\partial z} = -3x^2z^2 = \frac{\partial h}{\partial z} \Rightarrow h(z) = -x^2z^3[/tex]
So, [tex]f(x,y,z) = x^2y^3 - 2x^2z^3[/tex]
This answer doesn't check out. Taking the partial of f with respect to x, y, and z does not yield the initial equation. What am I missing? Is there a better way to go about this?
The correct answer turns out to be [tex]x^2y^3 - x^2z^3[/tex], which is my initial equation for f without h(z).
Thanks!
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