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人気のある微分積分 >

integral from 0 to 3 of xsqrt(x+1)

解

\int_{0}^{3} x x + 1 d x

解

\frac{116}{15}

+1

十進法表記

7.73333 \dots

解答ステップ

\int_{0}^{3} x x + 1 d x

u置換積分法を適用する

= \int_{1}^{4} (u - 1) u d u

拡張

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

= \int_{1}^{4} 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}^{4} u^{\frac{3}{2}} d u - \int_{1}^{4} u d u

\int_{1}^{4} u^{\frac{3}{2}} d u = \frac{62}{5}

\int_{1}^{4} u d u = \frac{14}{3}

= \frac{62}{5} - \frac{14}{3}

簡素化

\frac{62}{5} - \frac{14}{3} : \frac{116}{15}

= \frac{116}{15}

グラフ

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