# 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)

Attachment 20908

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. the mistake is that you have written $\frac{\partial \phi}{\partial y} = C_1^{ \prime} (y)$. this is wrong.
instead it should be $\frac{\partial \phi}{\partial y}= e^x cosy + C_1^{ \prime} (y)$

3. All is correct except for the last line:

$\varphi (x,y)=e^x\sin y +C_1(y)=e^x\sin y +C_2$

Why on earth do you write twice $e^x\sin y$ ?

Fernando Revilla

Edited: Sorry, I didn't see abhisekkgp's post.