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Find the area of the region bounded by y = x and circle x2 + y2 = 32 in the 1st quadrant.
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