The area bounded by the curves $$y = \left| x \right| - 1$$ and $$y = - \left| x \right| + 1$$ is-
A.
$$1$$
B.
$$2$$
C.
$$2\sqrt 2 $$
D.
$$4$$
Answer :
$$2$$
Solution :
The given lines are
$$\eqalign{
& y = x - 1;\,\,\,y = - x - 1; \cr
& y = x + 1\,{\text{and}}\,y = - x + 1 \cr} $$
which are two pairs of parallel lines and distance between the lines of each pair is $$\sqrt 2 .$$ Also non parallel lines are perpendicular. Thus lines represents a square
of side $$\sqrt 2 .$$
Hence, area $$ = {\left( {\sqrt 2 } \right)^2} = 2$$ sq. units.
Releted MCQ Question on Calculus >> Application of Integration
Releted Question 1
The area bounded by the curves $$y = f\left( x \right),$$ the $$x$$-axis and the ordinates $$x = 1$$ and $$x = b$$ is $$\left( {b - 1} \right)\sin \left( {3b + 4} \right).$$ Then $$f\left( x \right)$$ is-