5.5 Application of double integrals

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

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

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