Changing the order of integration

[Amaelle]

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!

 

[Orodruin]

Yes, it would be wrong. That would be the other part of the square in your figure.

 

[Amaelle]

Yes, it would be wrong. That would be the other part of the square in your figure.

I got it now, thanks a lot!