Find the area of the region {(x,y): x^{2} + y^{2} ≤ 4, x + y ≥ 2}

The equation of the given curves are

X^{2} + y^{2} = 4 (i)

X + y = 2 (ii)

Clearly X^{2} + y^{2} = 4 represents a circle X + y = 2 is the equation of a straight line cutting x and y axes at (0, 2) and (2, 0) respectively.

These are shown in the graph below:

The required area is given by

We have y_{1} = 2 – x and y_{2} =

the area of the region {(x,y): x^{2} + y^{2}≤ 4, x + y ≥ 2}is

43