- #1

gtfitzpatrick

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## Homework Statement

confirm that the given function is apotential for the given vector field

[itex]ln(x^{2} + y^{2}) for \frac{2x}{\sqrt{x^{2}+y^{2}}} \vec{i} + \frac{2y}{\sqrt{x^{2}+y^{2}}} \vec{j}[/itex]

## Homework Equations

## The Attempt at a Solution

the first thing i did was let my equation = [itex]P\vec{i}+Q \vec{j}[/itex]

then if they are conservative[itex]\frac{\partial P}{\partial y} = \frac{\partial Q}{\partial x} [/itex]

[itex]\frac{\partial P}{\partial y} = \frac{-2xy}{\sqrt{x^{2}+y^{2}}} [/itex]

and

[itex]\frac{\partial Q}{\partial x} = \frac{-2xy}{\sqrt{x^{2}+y^{2}}} [/itex]

so the vector field is conservative.

then

f(x,y) = [itex]\int P(x,y) dx[/itex] and f(x,y) = [itex]\int Q(x,y) dy[/itex]

from tables i get f(x,y) = 2([itex]\sqrt{x^2 + y^2}[/itex]

what am i doing wrong here? am i getting my integration wrong?