Question

What is the area of a plane figure bounded by the points of the lines max $(x,y)=1$ and $x^2+y^2=1$ ?

Answer 1

REF.Image.

Solution-

$max(x,y)=1$

$x^2+y^2=1$

Shaded Area = Area of square ABCD - $\frac{1}{4}$ Area of circle

$=1\times 1-\frac{1}{4}\pi (1{)}^2$

$=1-\frac{\pi }{4}$

$\simeq 0.214squnits.$