# Conservative field?

• Feb 23rd 2011, 09:40 AM
wilbursmith
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)

Attachment 20908

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
• Feb 23rd 2011, 10:11 AM
abhishekkgp
the mistake is that you have written $\frac{\partial \phi}{\partial y} = C_1^{ \prime} (y)$. this is wrong.
instead it should be $\frac{\partial \phi}{\partial y}= e^x cosy + C_1^{ \prime} (y)$
• Feb 23rd 2011, 10:18 AM
FernandoRevilla
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.