Problem integrating a double integral

In summary, the conversation is about integrating a partial derivative of a function u(x,y) and the confusion lies in the labeling of the equations. The speaker suggests referencing a math book for clarification and mentions that the answer should be u(x,y) for indefinite integrals.
  • #1
hoomanya
90
0
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.
 
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  • #2
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.
 
  • #3
MarcusAgrippa said:
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.
 
  • #4
Are you sure? That answer does not look right to me. u should be a function of two variables.
 
  • #5
MarcusAgrippa said:
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.
 
  • #6
If you are doing indefinite integrals, my guess is that the answer you want is u(x,y).
 

1. What is a double integral?

A double integral is a type of mathematical integration that involves integrating a function of two variables over a two-dimensional region. It is represented by the symbol ∫∫ or ∫∫f(x,y)dA.

2. What is the purpose of a double integral?

The purpose of a double integral is to find the volume under a surface that is defined by a function of two variables. It is also used to calculate the area of a two-dimensional region.

3. How is a double integral evaluated?

A double integral is evaluated by first determining the limits of integration for both variables. Then, the function is integrated with respect to one variable, while treating the other variable as a constant. This process is repeated for the other variable, and the two results are multiplied together to get the final value.

4. What are the common challenges in solving a double integral?

One of the common challenges in solving a double integral is determining the appropriate limits of integration. This requires a good understanding of the region of integration and the function being integrated. Another challenge is correctly setting up the integral, as the order of integration can affect the final result.

5. How is a double integral used in real-life applications?

Double integrals are used in various fields of science, such as physics, engineering, and economics. They are used to calculate the volume and mass of objects, as well as to find the center of mass of an object. They are also used in probability and statistics to calculate the joint probability of two events.

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