# double integration

• Jan 4th 2013, 10:12 PM
happymatthematics
double integration
integral integral |x-y|dydx where x is from 0 to 1 and y is from 0 to 1.
......
I don't know how to deal with this question because there is an absolute value.
I tried to split the range x to ( 0 to y and y to 1), but fail to get the correct answer. = =
Can anyone help me?
...
if you think my question typed is not clear, plz see the attached file.
• Jan 4th 2013, 10:59 PM
chiro
Re: double integration
Hey happymatthematics.

You need to split this into two integrals that are analytic.

Hint: When is x-y < 0 and when is x-y > 0? (This will help you find the limits to split the integral up)
• Jan 4th 2013, 11:24 PM
happymatthematics
Re: double integration
Attachment 26473
this is my thought of next step...
I split 0<y<1 into 0<y<x and x<y<1,
but it doesn't work ;(
I got 2/3 but it is not the answer.
How to analyze?

I don't know the intuition to do this question.
What criteria should be fulfilled when I split the integral into two integrals?
Thank you!
• Jan 5th 2013, 12:48 AM
chiro
Re: double integration
Show us your working out in detail for the two integrals.
• Jan 5th 2013, 05:52 AM
happymatthematics
Re: double integration
Attachment 26479
plz click the picture above to see my work.
Is this correct?
besides, this is my first time encountering this kind of questions,
I mean an absolute value inside an integral.
how to deal with a more complicated question?
can you give me a more complicated example with the intuition to solve this kind of problems?
sometimes I want to self-learn but cannot find similar questions in books.
I lack the intuitions to solve this kind of problems.
Thank you!
• Jan 5th 2013, 08:12 AM
hollywood
Re: double integration
There is a $\displaystyle y^2$ on the third line which should be $\displaystyle \frac{y^2}{2}$, but the line after that is ok.

You should look for problems where you can change the order of integration and do the integral both ways. So you should get the same result with y first as with x first. This problem is a special case where you had to divide the area into two parts.

- Hollywood