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人気のある微分積分 >

integral from-3 to 5 of xsqrt(4+x)

解

\int_{- 3}^{5} x 4 + x d x

解

\frac{412}{15}

+1

十進法表記

27.46666 \dots

解答ステップ

\int_{- 3}^{5} x 4 + x d x

u置換積分法を適用する

= \int_{1}^{9} (u - 4) u d u

拡張

(u - 4) u : u^{\frac{3}{2}} - 4 u

= \int_{1}^{9} u^{\frac{3}{2}} - 4 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_{1}^{9} u^{\frac{3}{2}} d u - \int_{1}^{9} 4 u d u

\int_{1}^{9} u^{\frac{3}{2}} d u = \frac{484}{5}

\int_{1}^{9} 4 u d u = \frac{208}{3}

= \frac{484}{5} - \frac{208}{3}

簡素化

\frac{484}{5} - \frac{208}{3} : \frac{412}{15}

= \frac{412}{15}

グラフ

人気の例

integral from 0 to t of (t-w)e^{3w}

\int_{0}^{t} (t - w) e^{3 w} d w

integral from 2 to 16 of 1/x

\int_{2}^{16} \frac{1}{x} d x

integral from 0 to θ of x*(2x)/(θ^2)

\int_{0}^{θ} x \cdot \frac{2 x}{θ ^{2}} d x

integral from 0 to 3 of x^3-4x^2+3x

\int_{0}^{3} x^{3} - 4 x^{2} + 3 x d x

integral from 1 to infinity of 1/(x^e)

\int_{1}^{\infty} \frac{1}{x ^{e}} d x