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人気のある微分積分 >

integral from 0 to 5 of xsqrt(1+x)

解

\int_{0}^{5} x 1 + x d x

解

\frac{2}{3} + \frac{72 6 - 2}{5} - 46

+1

十進法表記

25.74135 \dots

解答ステップ

\int_{0}^{5} x 1 + x d x

u置換積分法を適用する

= \int_{1}^{6} (u - 1) u d u

拡張

(u - 1) u : u^{\frac{3}{2}} - u

= \int_{1}^{6} u^{\frac{3}{2}} - u 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

= \int_{1}^{6} u^{\frac{3}{2}} d u - \int_{1}^{6} u d u

\int_{1}^{6} u^{\frac{3}{2}} d u = \frac{72 6 - 2}{5}

\int_{1}^{6} u d u = 46 - \frac{2}{3}

= \frac{72 6 - 2}{5} - (46 - \frac{2}{3})

簡素化

= \frac{2}{3} + \frac{72 6 - 2}{5} - 46

グラフ

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