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Next: 7.6 3重積分 Up: 確認問題解答 Previous: 7.4 広義積分   目次   索引

7.5 2重積分の応用

1.

(a) $ \displaystyle{\frac{3\pi}{4}}$ (b) $ \displaystyle{9(\frac{\pi}{12} - \frac{\sqrt{3}}{8})}$ (c) $ \displaystyle{2\pi}$

2.

(a) $ \displaystyle{2\pi}$ (b) $ \displaystyle{\frac{3\sqrt{3}}{2}}$ (c) $ \displaystyle{\frac{2\pi}{3}\left((a^{2} + 1)^{3/2} - 1\right)}$

3.

(a) $ \displaystyle{\pi}$ (b) $ \displaystyle{\frac{\pi}{2}}$