Question

Find the area of the region {(x, y) : x² + y² ≤ 4, x + y ≥ 2}

Answer 1

The equation of the given curves are

x² + y² = 4 (i)

x + y = 2 (ii)

Clearly x² + y² = 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

The area of the region {(x, y) : x² + y² ≤ 4, x + y ≥ 2} is \(\pi - 2\) sq. units.