5.6 Triple integrals

(a) $\displaystyle{\frac{1}{6}}$ (b) $\displaystyle{\frac{1}{6}(e-1)^3}$

(a) $\displaystyle{\frac{27 \pi(2\sqrt{2} - 1)}{2}}$ (b) $\displaystyle{\frac{4}{15}\pi abc\left(a^2 + b^2 + c^2\right)}$

(a) $\displaystyle{(\bar{x}, \bar{y}) = (\frac{1}{2}, \frac{2}{5})}$ (b) $\displaystyle{(\bar{x},\bar{y},\bar{z}) = (0,0,\frac{2a}{5})}$ (c) in the direction of the height $\displaystyle{\frac{h}{4}}$

(d) $\displaystyle{(\bar{x},\bar{y}) = (-\frac{a}{6},0)}$ (e) $\displaystyle{(\bar{x},\bar{y},\bar{z}) = (\frac{1}{3},\frac{1}{3},\frac{1}{3})}$ (f) $\displaystyle{(\bar{x},\bar{y}) = (-\frac{6a}{5(3\pi - 2)},0)}$