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 itīs "potential function" (Donīt know if itīs the correct translation but maybe youīll get it from my attempt)

I get an extra 2 in the answer and I donīt know why. This is extremely irritating as I get stuck with small problems. Takes a lot of time which I donīt 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