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# 计算机系统概述 | ||
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![计算机系统概述](1.计算机系统概述.png) | ||
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# 基本性质 | ||
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* [定理内容](#定理内容) | ||
* [经典例题](#经典例题) | ||
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## 定理内容 | ||
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\iint_D{1}d\sigma = \iint_D{}d\sigma = A ,其中 A 为 D 的面积. | ||
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当 f(x , y) 在有界闭区间 D 上可积时, f(x , y) 在 D 上必有界. | ||
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设 k_1 , k_2 为常数,则 \iint_D{[{k_1}f(x , y) \pm {k_2}g(x , y)]}d\sigma = k_1\iint_D{f(x , y)}d\sigma \pm k_2\iint_D{g(x , y)}d\sigma . | ||
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设 f(x , y) 在有界闭区间 D 上可积,且 D_1 \cup D_2 = D , D_1 \cap D_2 = \varnothing ,则 \iint_D{f(x , y)}d\sigma = \iint_{D_1}{f(x , y)}d\sigma + \iint_{D_2}{f(x , y)}d\sigma . | ||
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当 f(x , y) , g(x , y) 在有界闭区间 D 上可积时,若在 D 上有 f(x , y) \le g(x , y) ,则 \iint_D{f(x , y)}d\sigma \le \iint_D{g(x , y)}d\sigma . | ||
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设 M , m 分别是 f(x , y) 在有界闭区域 D 上的最大值和最小值, A 为 D 的面积,则 mA \le \iint_D{f(x , y)}d\sigma \le MA . | ||
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设函数 f(x , y) 在有界闭区域 D 上连续, A 为 D 的面积,则在 D 上至少存在一点 (\xi , \eta) ,使得 \iint_D{f(x , y)}d\sigma = f(\xi , \eta)A . | ||
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## 经典例题 | ||
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