Find all maxima and minima of the function $$$y = x{\left( {x - 1} \right)^2},0 \le x \le 2$$$
Also determine the area bounded by the curve $$y = x{\left( {x - 1} \right)^2}$$,
the $$y$$-axis and the line $$y-2$$.

$$ABC$$ is a triangular park with $$AB=AC=100$$ $$m$$. A television tower stands at the midpoint of $$BC$$. The angles of elevetion of the top of the tower at $$A, B, C$$ are 45$$^ \circ $$, 60$$^ \circ $$, 60$$^ \circ $$, respectively. Find the height of the tower.

Evaluate $$\int {\left( {\sqrt {\tan x} + \sqrt {\cot x} } \right)dx} $$

The value of $$\int\limits_{ - 2}^2 {\left| {1 - {x^2}} \right|dx} $$ is ...............