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How do I find the potential function of this conservative vector field (It is conservative isn't it?? I did check, but i might've messed that up too!).

[itex] \int (2x-3y-1)dx - (3x+y-5)dy [/itex]

I know to break the function:

[itex] F(x,y)= (2x-3y-1)i - (3x+y-5)j [/itex]

apart and integrate each part WRT x or y like:

[itex] f(x,y)= \int (2x-3y-1)dx [/itex]

[itex] f(x,y)= \int (3x+y-5)dy [/itex]

To get:

[itex] x^2-3xy-x+g(y)+K[/itex]

and

[itex] -3xy + y^2/2 - 5y +h(x) + K[/itex]

Respectivlly. K being the constant of integration, but then i don't know how to combine/cancle/manipulate thoes to get one function....

I thought (and my book seems to show) that you have to find what g(y) and h(x) are but I don't know how to do that, and even if I did I would again be stuck and put them together.

Thanks,

-Burg

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# Potential function of conservative vector field

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