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人気のある微分積分 >

integral from 0 to 2 of x/(sqrt(x^2+5))

解

\int_{0}^{2} \frac{x}{x ^{2} + 5} d x

解

3 - 5

+1

十進法表記

0.76393 \dots

解答ステップ

\int_{0}^{2} \frac{x}{x ^{2} + 5} d x

u置換積分法を適用する

= \int_{5}^{9} \frac{1}{2 u} d u

定数を除く:

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

= \frac{1}{2} \cdot \int_{5}^{9} \frac{1}{u} d u

べき乗則を適用する

= \frac{1}{2} [2 u^{\frac{1}{2}}]_{5}^{9}

累乗根の規則を適用する:

a^{\frac{1}{n}} = n a

= \frac{1}{2} [2 u]_{5}^{9}

限度を計算する:

6 - 25

= \frac{1}{2} (6 - 25)

簡素化

= 3 - 5

グラフ

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