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Don't understand your notation: what is the 0s in front of integral sign?

The first one seems to be describing the line y=x

The whole region is a semicircle of radius one, pierced by y=x

Thanks, but i"m still lost.
What would the interval of the region be?

First one 0

Second one 0

Oh, so I don't have to write a notation that combines the two iterated integrals as one?

Okay, thanks a lot!