The area of the region described by A = {(x,y) :x²+y²≤ 1 andy²≤ 1 x} is :??

The intersection point can be obtained by putting y² = 1-x  in x² +y² = 1
So x² +1-x = 1
Or x(x-1) =0
So x = 1 and x = 0

Hence the shaded area is half circle + area between ABC
= $\frac{\mathrm{\pi }}{2}(1{)}^2 + 2{\int }_0^1\sqrt{1-x}dx$
= $\frac{\mathrm{\pi }}{2} +2[-\frac{2}{3}(1-x{)}^{3/2}{{]}_0}^1 =\frac{\mathrm{\pi }}{2} +\frac{4}{3}$