5.6 Triple integrals

1.

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

2.

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

3.

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

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