무리함수 회전체 부피

$\displaystyle \pi \int _{0} ^{6} \left\{ \sqrt{x + 2} \right\} ^{2} - \pi \int _{0} ^{2} \left\{ - x + 2 \right\} ^{2} - \pi \int _{2} ^{6} \left\{ \sqrt{2 x - 4} \right\} ^{2}$ $\displaystyle = \pi \left[ \frac{1}{2} x ^{2} + 2 x \right] _{0} ^{6} - \pi \left[ - \frac{1}{2} x ^{2} + 2 x \right] _{0} ^{2} - \pi \left[ x ^{2} - 4 x \right] _{2} ^{6}$ $= \pi ( 18 + 12 + 2 - 4 - 12 - 4 ) = 12 \pi$