Find the area bounded by the curves, $${x^2} + {y^2} = 25,\,4y = \left| {4 - {x^2}} \right|$$ and $$x=0$$ above the $$x$$-axis.

Sketch the region bounded by the curves $$y = \sqrt {5 - {x^2}} $$ and $$y = \left| {x - 1} \right|$$ and find its area.

Find the area of the region bounded by the $$x$$-axis and the curves defined by $$$y = \tan x, - {\pi \over 3} \le x \le {\pi \over 3};\,\,y = \cot x,{\pi \over 6} \le x \le {{3\pi } \over 2}$$$

Find the area bounded by the $$x$$-axis, part of the curve $$y = \left( {1 + {8 \over {{x^2}}}} \right)$$ and
the ordinates at $$x=2$$ and $$x=4$$. If the ordinate at $$x=a$$ divides the area into two equal parts, find $$a$$.