Yep, but should I draw it according to these 'lines' above?
Yes. A slight correction: if you use only integrals to describe the area and you switch the order of integration, you will need three integrals, not two, although one of these is a rectangle.
That's ok, my teacher did it once only with integrals.
Could you tell me what's the easiest way to draw without calculator?
Square both sides and you get , or , which is a circle centered at the origin with radius . Note that is only part of this circle. The best way to draw it would be with pencil and compass.