Problem integrating a double integral

[hoomanya]

Hi, could you please help with the integration of this equation:
$$\int_{x}\int_{y}\frac{\partial}{\partial y}\left(\frac{\partial u}{\partial x}\right)\,dydx$$
where $u(x,y)$ . From what I remember, you first perform the inner integral i.e. $\int_{y}\frac{\partial}{\partial y}\left(\frac{\partial u}{\partial x}\right)dy$ but I am not really sure where to go from there. I'm too old for homework so please don't assume that it is. Thank you in advance. A reference would be good anough too.

 

[MarcusAgrippa]

Try reading Marsden and Tromba, Vector Calculus. Or any other freshman math book, like Thomas and Finney.

You have not been very explicit in what you ask. It is possible to write down a general symbolic expression for this integral. But you probably have something more particular in mind, requiring a domain of integration and a function u to be specified.

 

[hoomanya]

Try reading Marsden and Tromba, Vector Calculus. Or any other freshman math book, like Thomas and Finney.

You have not been very explicit in what you ask. It is possible to write down a general symbolic expression for this integral. But you probably have something more particular in mind, requiring a domain of integration and a function u to be specified.

Hi, thanks. I will have a look at the books. Actually, I am after a general response. I have the results as u(x)+u(y) but not sure how that has come about.

 

[MarcusAgrippa]

Are you sure? That answer does not look right to me. u should be a function of two variables.

 

[hoomanya]

Are you sure? That answer does not look right to me. u should be a function of two variables.

That's what I thought. I might be reading the text I am reading wrong as the equations are not labelled correctly. Thanks. Good to know something else might be the problem.

 

[MarcusAgrippa]

If you are doing indefinite integrals, my guess is that the answer you want is u(x,y).