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人気のある微分積分 >

integral from 6 to 7 of (xsqrt(x-6))

解

\int_{6}^{7} (x x - 6) d x

解

\frac{22}{5}

+1

十進法表記

4.4

解答ステップ

\int_{6}^{7} x x - 6 d x

u置換積分法を適用する

= \int_{0}^{1} (u + 6) u d u

拡張

(u + 6) u : u^{\frac{3}{2}} + 6 u

= \int_{0}^{1} u^{\frac{3}{2}} + 6 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} 6 u d u

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

\int_{0}^{1} 6 u d u = 4

= \frac{2}{5} + 4

簡素化

\frac{2}{5} + 4 : \frac{22}{5}

= \frac{22}{5}

グラフ

人気の例

integral from 1 to x^2 of 2x^2y(x+y)

\int_{1}^{x^{2}} 2 x^{2} y (x + y) d y

integral from 1 to e^8 of 4/x

\int_{1}^{e^{8}} \frac{4}{x} d x

integral from-1 to 2 of (2x+1)(2x-1)

\int_{- 1}^{2} (2 x + 1) (2 x - 1) d x

integral from 0 to 1 of 8x^7(6-x^8)

\int_{0}^{1} 8 x^{7} (6 - x^{8}) d x

integral from-3 to 4 of (1-x)

\int_{- 3}^{4} (1 - x) d x