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人気のある微分積分 >

integral from 9 to 18 of xsqrt(x-9)

解

\int_{9}^{18} x x - 9 d x

解

\frac{1296}{5}

+1

十進法表記

259.2

解答ステップ

\int_{9}^{18} x x - 9 d x

u置換積分法を適用する

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

拡張

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

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

\int_{0}^{9} u^{\frac{3}{2}} d u = \frac{486}{5}

\int_{0}^{9} 9 u d u = 162

= \frac{486}{5} + 162

簡素化

\frac{486}{5} + 162 : \frac{1296}{5}

= \frac{1296}{5}

グラフ

人気の例

integral from 0 to 1 of x^2(x^3-3)^4

\int_{0}^{1} x^{2} (x^{3} - 3)^{4} d x

integral from 0 to 7 of x/(sqrt(4+3x))

\int_{0}^{7} \frac{x}{4 + 3 x} d x

integral from-4 to 4 of (16x-(x^3)/3)

\int_{- 4}^{4} (16 x - \frac{x ^{3}}{3}) d x

integral from 1 to t of xe^{-x^2}

\int_{1}^{t} x e^{- x^{2}} d x

integral from 2 to 5 of 4/(sqrt(x))

\int_{2}^{5} \frac{4}{x} d x