Q43 of 123 Page 22

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

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



We have y1 = 2 – x and y2 =









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


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