Changing the order of integration

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SUMMARY

The discussion centers on changing the order of integration in a double integral problem involving the limits 0 ≤ y ≤ 1 and 0 ≤ x ≤ y². The participants confirm that altering the limits to 0 ≤ y ≤ 1 and y² ≤ x ≤ 1 is incorrect, as it represents a different region of integration. The consensus emphasizes the importance of maintaining the correct geometric interpretation of the area defined by the original limits.

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Amaelle
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Homework Statement
Calculate the following integral (look at the image)
Relevant Equations
Double integrals
Greetings!
As mentionned my aim is to change the order of integral, and I totally agree with the solution I just have one question:
as you can see they have put
0<=y<=1 and 0<=x<=y^2
but would it be wrong if I put
0<=y<=1 and y^2<=x<=1?
Thank you!
1622822248789.png
 
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Yes, it would be wrong. That would be the other part of the square in your figure.
 
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Orodruin said:
Yes, it would be wrong. That would be the other part of the square in your figure.
I got it now, thanks a lot!
 

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