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Next: 7.3 累次積分 Up: 確認問題解答 Previous: 6.9 条件付極値   目次   索引

7.2 累次積分

1.

(a) $ \displaystyle{0}$ (b) $ \displaystyle{\frac{7}{6}}$ (c) $ \displaystyle{\frac{11}{40}}$ (d) $ \displaystyle{2}$ (e) $ \displaystyle{\frac{1}{12}}$

2.

(a) $ \displaystyle{\int_{0}^{1}\int_{y}^{\sqrt{y}}f(x,y)dx dy}$ (b) $ \displaystyle{\int_{0}^{1}\int_{\sqrt{x}}^{1}f(x,y)dy dx}$

(c) $ \displaystyle{\int_{0}^{1}\int_{0}^{2y}f(x,y)dx dy + \int_{1}^{3}\int_{0}^{3-y}f(x,y)dx dy}$

3.

(a) $ \displaystyle{\frac{1}{3}}$ (b) $ \displaystyle{\frac{5}{2}}$ (c) $ \displaystyle{\frac{\pi}{2}}$