X 2+y 2 = x+y, and the formula (x-0.5) 2+(y-0.5) 2 = 0.5.

This is an arc with the center p (0.5,0.5) and the radius Sqrt(2)/2. Where Sqrt is the root symbol.

The intersection of the arc and the coordinate axis is A(0, 1) and B( 1, 0).

The area enclosed by the arc and the coordinate axis = the area of the circle -2* the area of the arc between the arc AO and the y axis.

From the perspective of triangular relationship: PAO is a right angle

The arch area is: 1/4 circle area-triangle PAO area =1/4 * pi * 0.5-0.5 * 0.5 = pi/8-0.25.

So the area enclosed by the arc and the coordinate axis = the area of the circle -2* the area of the arc between the arc AO and the y axis =PI*0.5-2*(PI/8-0.25)=PI/4+0.5.

As can be seen from the symmetry, the area enclosed by the curve is four times the above area.

That is π+2.