Let the functions f : R $$ \to $$ R and g : R $$ \to $$ R be defined by

f(x) = e^{x $$-$$ 1} $$-$$ e^{$$-$$|x $$-$$ 1|}

and g(x) = $${1 \over 2}$$(e^{x $$-$$ 1} + e^{1 $$-$$ x}).

The the area of the region in the first quadrant bounded by the curves y = f(x), y = g(x) and x = 0 is

The area of the region

{(x, y) : xy $$ \le $$ 8, 1 $$ \le $$ y $$ \le $$ x²} is

Area of the region

$$\left\{ {\left( {x,y} \right) \in {R^2}:y \ge \sqrt {\left| {x + 3} \right|} ,5y \le x + 9 \le 15} \right\}$$

is equal to

The area enclosed by the curves $$y = \sin x + {\mathop{\rm cosx}\nolimits} $$ and $$y = \left| {\cos x - \sin x} \right|$$ over the interval $$\left[ {0,{\pi \over 2}} \right]$$ is