Answer :

To find area of in first quadrant enclose by the circle

X2 + y2 = 32 …(i)


And y = x …(ii)


Solving these two equations, we get


Or 2X2 = 32


Or X2 = 16


Or x = 4


y = 4


Equation (i) is a circle with centre (0, 0) and meets axes at A (±4√2, 0), (0,±4√2). And y = x is a line passes through (0, 0) and intersect circle at B (4, 4).


These are shown in the graph below:



Region OABO = Region OCBO + Region CABC








The area of the region bounded by y = x and circle X2 + y2 = 32 is


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