What is the area of a plane figure bounded by the points of the lines max (x, y) = 1 and x2 + y2 = 1 ?
Answer & explanation
Correct answer: option 3
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