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# The area of the region described by A={$(x,y):(x^2+y^2\leq 1$ and $y^2\leq 1-x$}

$\begin{array}{1 1}(A)\;\large\frac{\pi}{2}+\frac{4}{3}\\(B)\;\large\frac{\pi}{2}-\frac{4}{3}\\(C)\;\large\frac{\pi}{2}-\frac{2}{3}\\(D)\;\large\frac{\pi}{2}+\frac{2}{3}\end{array}$

$\large\frac{\pi}{2}+\frac{4}{3}$
Hence (A) is the correct answer.