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人気のある微分積分 >

integral from 1 to 2 of (4+x)/x

解

\int_{1}^{2} \frac{4 + x}{x} d x

解

4 ln (2) + 1

+1

十進法表記

3.77258 \dots

解答ステップ

\int_{1}^{2} \frac{4 + x}{x} d x

拡張

\frac{4 + x}{x} : \frac{4}{x} + 1

= \int_{1}^{2} \frac{4}{x} + 1 d x

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{1}^{2} \frac{4}{x} d x + \int_{1}^{2} 1 d x

\int_{1}^{2} \frac{4}{x} d x = 4 ln (2)

\int_{1}^{2} 1 d x = 1

= 4 ln (2) + 1

グラフ

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