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人気のある微分積分 >

integral from 9 to 10 of (xsqrt(x-9))

解

\int_{9}^{10} (x x - 9) d x

解

\frac{32}{5}

+1

十進法表記

6.4

解答ステップ

\int_{9}^{10} x x - 9 d x

u置換積分法を適用する

= \int_{0}^{1} (u + 9) u d u

拡張

(u + 9) u : u^{\frac{3}{2}} + 9 u

= \int_{0}^{1} u^{\frac{3}{2}} + 9 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_{0}^{1} u^{\frac{3}{2}} d u + \int_{0}^{1} 9 u d u

\int_{0}^{1} u^{\frac{3}{2}} d u = \frac{2}{5}

\int_{0}^{1} 9 u d u = 6

= \frac{2}{5} + 6

簡素化

\frac{2}{5} + 6 : \frac{32}{5}

= \frac{32}{5}

グラフ

人気の例

integral from-3 to 3 of sqrt(7+2t^2)(8t)

\int_{- 3}^{3} 7 + 2 t^{2} (8 t) d t

integral from 0 to 1 of e^{3t}

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integral from 0 to 2pi of 4cos(t)sin(t)

\int_{0}^{2 π} 4 cos (t) sin (t) d t

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\int_{0}^{x} \frac{1}{2} sin (t) d t

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