The lengths of the sides of a triangle are 10 + x², 10 + x² and 20 $$-$$ 2x². If for x = k, the area of the triangle is maximum, then 3k² is equal to :

If $${\cos ^{ - 1}}\left( {{y \over 2}} \right) = {\log _e}{\left( {{x \over 5}} \right)^5},\,|y| < 2$$, then :

The value of the integral

$$\int\limits_{ - 2}^2 {{{|{x^3} + x|} \over {({e^{x|x|}} + 1)}}dx} $$ is equal to :