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人気のある微分積分 >

integral from-1 to 3 of 5xsqrt(x+1)

解

\int_{- 1}^{3} 5 x x + 1 d x

解

\frac{112}{3}

+1

十進法表記

37.33333 \dots

解答ステップ

\int_{- 1}^{3} 5 x x + 1 d x

定数を除く:

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

= 5 \cdot \int_{- 1}^{3} x x + 1 d x

u置換積分法を適用する

= 5 \cdot \int_{0}^{4} (u - 1) u d u

拡張

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

= 5 \cdot \int_{0}^{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

= 5 (\int_{0}^{4} u^{\frac{3}{2}} d u - \int_{0}^{4} u d u)

\int_{0}^{4} u^{\frac{3}{2}} d u = \frac{64}{5}

\int_{0}^{4} u d u = \frac{16}{3}

= 5 (\frac{64}{5} - \frac{16}{3})

簡素化

5 (\frac{64}{5} - \frac{16}{3}) : \frac{112}{3}

= \frac{112}{3}

グラフ

人気の例

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