I have following question:

Evaluate $\iint_{R} \sqrt{|y-x^2|} dx dy$

where $R=[-1,1;0,2]$

I am not familiar with notation for the region $R$. My guess is that $R$ represents a rectangle.

Does it represent rectangle with vertices $\{(-1,0),(1,0),(1,2),(-1,2)\}$ or it represents something else?

Please help.

  • 2
    $\begingroup$ I believe that you are correct. It appears that you are integrating from -1 to 1 along the x-axis and then from 0 to 2 along the y-axis although this is not standard notation. $\endgroup$ – RedShift Sep 30 '16 at 16:51
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    $\begingroup$ I don't think the notation given in your question is standard but as @RedShift has pointed out it might be a notation for a rectangle. $\endgroup$ – Math Lover Sep 30 '16 at 16:52
  • 1
    $\begingroup$ @RedShift That's what I am assuming for now in absence of clarity. $\endgroup$ – Prince Kumar Sep 30 '16 at 16:58
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    $\begingroup$ I think the notation is unclear, because as plausible as @RedShift 's interpretation is (and I agree with it) nothing really says that the first part of R (-1, 1) belongs to the x axis in any way. Given that it's a double integral, you might also consider this first pair of numbers to belong to the first integral symbol, which is the outer of the two integrals, which actually integrates along the y axis. Ask the person who asked you this question for clarification. $\endgroup$ – null Sep 30 '16 at 17:19
  • $\begingroup$ @null Unfortunately for me, this is a question that was asked in a competitive exam last year. There is no way to know what they meant by that notation. $\endgroup$ – Prince Kumar Sep 30 '16 at 18:24

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