Question

The area enclosed by the curves $|y+x|\le 1,|y-x|\le 1$ and $2x^2+2y^2=1$ is

• A. $(2+\frac{\pi }{2})$ sq. units
• B. $(2-\frac{\pi }{2})$ sq. units
• C. $(3+\frac{\pi }{2})$ sq. units
• D. $(3-\frac{\pi }{2})$ sq.units

Answer 1

The correct option is B $(2-\frac{\pi }{2})$ sq. units

The curves $y+x\le 1$$and$|y - x|\leq 1$formasquare$ABCD$and$2x^{2} + 2y^{2} = 1$isacircleofradius$\dfrac {1}{\sqrt {2}}$andcentre$(0, 0)$.Therefore,requiredarea$=$Areaofsquare$-$Areaofcircle$= \left (2 -\dfrac {\pi}{2}\right ) $ sq. units