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人気のある微分積分 >

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

解

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

解

\frac{16}{15}

+1

十進法表記

1.06666 \dots

解答ステップ

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

u置換積分法を適用する

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

拡張

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

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

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

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

= \frac{2}{5} + \frac{2}{3}

簡素化

\frac{2}{5} + \frac{2}{3} : \frac{16}{15}

= \frac{16}{15}

グラフ

人気の例

integral from 0 to 5 of sqrt(1+x)

\int_{0}^{5} 1 + x d x

integral of 1/(sqrt(x^2+8x+25))

\int \frac{1}{x ^{2} + 8 x + 25} d x

d/(d{x)}({y}^2sin({x}{z}))

\frac{d}{d x} (y^{2} sin (x z))

integral of 6sec^3(x)

\int 6 sec^{3} (x) d x

derivative of 2/(x-11)

\frac{d}{d x} (\frac{2}{x - 11})