Find the area of the region bounded by the curve y = √1 – x2, line y = x and the positive x - axis.
To find the area of the region bounded by
y = √1 – x2 …(i)
X2 + y2 = 1
X = y …(ii)
On solving the equation (i) and (ii),
Or X2 + x2 = 1
Or 2X2 = 1
Or x =
Equation (i) represents a circle (0,0) and meets axes at (±1,0), (0,±1).
Equation (ii) represents a line passing through B and and they are also points of intersection.
These are shown in the graph below:
Required area = Region OABO
= Region OCBO + Region CABC
The area of the region bounded by the curve y = √1 – x2, line y = x is