# Math Help - Conservative field?

1. ## Conservative field?

Hi.

Just checked my answer on a question from my workbook on line integrals. Almost nailed it but not quite.

Question is this.

Verify that the following vectorfield is conservative and determine it´s "potential function" (Don´t know if it´s the correct translation but maybe you´ll get it from my attempt)

I get an extra 2 in the answer and I don´t know why. This is extremely irritating as I get stuck with small problems. Takes a lot of time which I don´t have. So what did i miss?

-WS

2. Hi

You are getting $\varphi(x,y)=e^x \sin y + C_1(y)$

Now on one hand $\frac{\partial \varphi}{\partial y} = e^x \cos y + C_1'(y)$

on the other hand $\frac{\partial \varphi}{\partial y} = e^x \cos y$

therefore $C_1'(y) = 0$ which means that $C_1(y) = C_1$ and finally $\varphi(x,y)=e^x \sin y + C_1$

3. Yes of course. Thank you! I tried to follow the method from an example in my workbook mechanically without really understanding the procedure. I searched the web and found it easier to understand this with another notation for partial derivatives. But your explanation makes even more sense.

-WS