What is the area of a plane figure bounded by the points of the lines max (x, y) = 1 and x² + y² = 1 ?

$\frac{\pi}{4}$ sq. units

By definition the lines max, (x, y) = 1 means.

x = 1 and y ≤ 1 or y = 1 and x ≤ 1

Required area

$=\int\limits_0^1\left[1-\sqrt{1-x^2}\right] d x$

$=\left[x-\frac{x}{2} \sqrt{1-x^2}-\frac{1}{2} \sin ^{-1} x\right]_0^1$

$=1=0=\frac{1}{2}\left(\frac{\pi}{2}\right) = 1 = \frac{\pi}{4}$ sq. units