5.5 Application of double integrals

1.

(a) $${\frac{3\pi}{32}}$$(b) $${\frac{a^2 \pi}{2}}$$(c) $${4\pi - \frac{3}{2}}$$

2.

(a) $${4 \pi a^2}$$(b) $${\frac{2\pi}{3}[(1+a^2)^{\frac{3}{2}} - 1]}$$ (c) $${8a^2}$$(d) $${\pi k^{2}m\sqrt{m^2 + 1}}$$

3.

(a) $${\frac{2a^3}{3}}$$(b) $${\frac{54}{105}}$$(c) $${-\frac{4a^3}{3}(\frac{2}{3} - \frac{\pi}{2})}$$(d) $${\frac{2}{9}}$$