If x³dy + xy dx = x²dy + 2y dx; y(2) = e and
x > 1, then y(4) is equal to :

The area (in sq. units) of the region

{ (x, y) : 0 $$ \le $$ y $$ \le $$ x² + 1, 0 $$ \le $$ y $$ \le $$ x + 1,
$${1 \over 2}$$ $$ \le $$ x $$ \le $$ 2 } is :

$$\int\limits_{ - \pi }^\pi {\left| {\pi - \left| x \right|} \right|dx} $$ is equal to :

Consider a region R = {(x, y) $$ \in $$ R : x² $$ \le $$ y $$ \le $$ 2x}. if a line y = $$\alpha $$ divides the area of region R into two equal parts, then which of the following is true?