double integral

[Bill Kekesis]

can someone explain me step by step solution to this double integral?
I know the result is 288000

 

[tkhunny]

1) I sincerely hope the direct and consensus answer to your question is "no". You must do work for yourself. We can help you on your way.
2) That was a terrible jpg. I snipped it for you. Please figure out how to make smaller ones or just enter the LaTeX or whatever math rendering language may be familiar to you.
3) I presume the absolute values are the problem? Get rid of them. Consider the line x = y vs. your region.

 

[HallsofIvy]

Could you use some help rather than a step by step solution?

Do you see that |x- y|, not a "smooth function", is a problem? I would break this into two integrals, one with x> y , the other with y> x. The region is y from 0 to 120, x from 0 to 60. The line y= x runs from (0,0) to (60, 60). Below that line, x is larger so |x- y|= x- y, above that line |x- y|= y- x.

 

[Bill Kekesis]

ok thank u I think I figured it out is that correct?

 

[Steven G]

Why do you still have so many absolute value bars even though you did not need them? In the end, you did get the correct result!

 

[tkhunny]

The idea is to get rid of the absolute values. You cannot do that with a region that lives on both sides of x = y.

Sometimes, it helps to reverse the order of integration. Not always. Certainly not mandatory in many cases.

Think on this. . Most importantly, notice that the absolute values are GONE.

 

[Bill Kekesis]

ok thank u I just dont understand why u can change the order of integration, not only with this particular integral but in general

 

[Bill Kekesis]

Anyway I searched a bit more on changing the order of integration and the most usual cases that it is possible is when we have rectangles and triangles and I think I understand why

 

[HallsofIvy]

I don't know what you mean by "when we have rectangles and triangles". Any region of integration can be reduced to limits of integrations over rectangles.