Found an almost analog problem, that deals whit double integrals and changeint the variables to polar cordinates.

The task is to calculate an integral

Where D is a half circle bounded by a circle

and the x axis.

This is a solved example from a book.

So the first thing they do is transform the formula of the circuit into polar coordinates.

So

So in the end they get:

I've drawn the half circle in the first quadrant. An then again my question, how where the limits 0 to

defined?

Why aren't the limits from 0 to

? That's a half circle then.