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人気のある微分積分 >

integral from 0 to 18 of x/(sqrt(9+4x))

解

\int_{0}^{18} \frac{x}{9 + 4 x} d x

解

\frac{45}{2}

+1

十進法表記

22.5

解答ステップ

\int_{0}^{18} \frac{x}{9 + 4 x} d x

u置換積分法を適用する

= \int_{3}^{9} \frac{u ^{2} - 9}{8} d u

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{8} \cdot \int_{3}^{9} u^{2} - 9 d u

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

= \frac{1}{8} (\int_{3}^{9} u^{2} d u - \int_{3}^{9} 9 d u)

\int_{3}^{9} u^{2} d u = 234

\int_{3}^{9} 9 d u = 54

= \frac{1}{8} (234 - 54)

簡素化

\frac{1}{8} (234 - 54) : \frac{45}{2}

= \frac{45}{2}

グラフ

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