The minimum value of the function $$f\left( x \right) = {1 \over 3}x\left( {{x^2} - 3} \right)\,\,$$ in the interval $$ - 100 \le x \le $$ $$100$$ occurs at $$x=$$ __________.

The integral $$\,\,{1 \over {2\pi }}\int {\int_D {\left( {x + y + 10} \right)dxdy\,\,} } $$ where $$D$$ denotes the disc: $${x^2} + {y^2} \le 4,$$ evaluates to _________.

The region specified by
$$\left\{ {\left( {\rho ,\varphi ,{\rm Z}} \right):3 \le \rho \le 5,\,\,{\pi \over 8} \le \phi \le {\pi \over 4},\,\,3 \le z \le 4.5} \right\}$$ in cylindrical coordinates has volume of ___________.

A triangle in the $$xy-$$plane is bounded by the straight lines $$2x=3y, y=0$$ and $$x=3.$$ The volume above the triangle and under the plane $$x+y+z=6Z$$ is ________.