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can someone please help me understand how to find the 'new' limits for double integration. I know that you have to split up the area and fix x or y. If you can go through an example with me then I would be grateful as I keep getting this wrong. We have only been taught how to work out the area of a triangle and so a quadrilateral makes no sense to me.... Btw please don’t give 'genera;' advice because I seriously won’t get it. I have looked in my books/lecture notes but it’s all just general theory which isn’t helpful.

Example question: By making an appropriate substitution, find the area of D and check the substitution is a 1-1 transformation by finding the inverse explicitly.

$$ \iint_D \exp{[xy(x-y)]} (x^2-y^2) {\rm d}x\, {\rm d}y$$

Here is the diagram: enter image description here Thanks for the help!

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    You've asked quite a number of questions but haven't accepted any of the answers. Were none of them satisfactory? Also, the image requires two clicks to get to -- you have enough reputation to include it directly in the question.2011-05-25
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    There seem to be two different questions here -- one is to calculate the area of $D$, which would involve integrating $1$ over $D$, and the other is to integrate $\exp{[xy(x-y)]} (x^2-y^2)$ over $D$ -- which one are you trying to solve? Or both?2011-05-25
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    Sorry - I'm new here! How do you accept an answer? How do you attach a pic directly? I never knew I could. And I just realised that my post did not paste properly... I will adjust this tomorrow! So sorry about that.2011-05-26
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    @user4645: You can accept an answer by clicking on the checkmark symbol next to it. You can attach an image by clicking on the corresponding icon (the one next to the "binary" symbol) in the toolbar above the edit textfield.2011-05-26
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    checkmark symbol???? ive made a new post instead to clarify my problems. i think its easier that way. someone please close this thread...2011-05-27
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    @user4645: That's not how this site works. Please read the FAQ (http://math.stackexchange.com/faq).2011-05-27

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