3.10 Application of definite integrals

1.
(a) $\displaystyle{\frac{9}{2}}$ (b) $\displaystyle{\frac{1}{12}}$ (c) $\displaystyle{\frac{22}{3}}$ (d) $\displaystyle{\frac{4}{3}}$ (e) $\displaystyle{36}$ (f) $\displaystyle{2}$
2.
(a) $\displaystyle{\frac{\pi}{3}}$ (b) $\displaystyle{\frac{1944\pi}{5}}$ (c) $\displaystyle{\frac{5\pi}{14}}$ (d) $\displaystyle{\frac{72\pi}{5}}$
3.
(a) $\displaystyle{2\sqrt{5}}$ (b) $\displaystyle{296}$ (c) $\displaystyle{4\sqrt{3} + 2\log\vert 2+\sqrt{3}\vert}$ (d) $\displaystyle{\sqrt{2}(e^{4\pi} - 1)}$