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人気のある微分積分 >

integral from 4 to 6 of x^2sqrt(x-4)

解

\int_{4}^{6} x^{2} x - 4 d x

解

\frac{3824 2}{105}

+1

十進法表記

51.50431 \dots

解答ステップ

\int_{4}^{6} x^{2} x - 4 d x

u置換積分法を適用する

= \int_{0}^{2} (u + 4)^{2} u d u

拡張

(u + 4)^{2} u : u^{\frac{5}{2}} + 8 u^{\frac{3}{2}} + 16 u

= \int_{0}^{2} u^{\frac{5}{2}} + 8 u^{\frac{3}{2}} + 16 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}^{2} u^{\frac{5}{2}} d u + \int_{0}^{2} 8 u^{\frac{3}{2}} d u + \int_{0}^{2} 16 u d u

\int_{0}^{2} u^{\frac{5}{2}} d u = \frac{16 2}{7}

\int_{0}^{2} 8 u^{\frac{3}{2}} d u = \frac{64 2}{5}

\int_{0}^{2} 16 u d u = \frac{64 2}{3}

= \frac{16 2}{7} + \frac{64 2}{5} + \frac{64 2}{3}

簡素化

\frac{16 2}{7} + \frac{64 2}{5} + \frac{64 2}{3} : \frac{3824 2}{105}

= \frac{3824 2}{105}

グラフ

人気の例

integral from 2 to 4 of (xy^2+x^2+y+4)

\int_{2}^{4} (x y^{2} + x^{2} + y + 4) d y

integral from-5 to-3 of sqrt(x^2-4)

\int_{- 5}^{- 3} x^{2} - 4 d x

integral from 0 to 4 of sqrt(x)(3-5x)

\int_{0}^{4} x (3 - 5 x) d x

integral from 0 to 8 of 6xln(x)

\int_{0}^{8} 6 x ln (x) d x

integral from 0.5 to 1 of 2x

\int_{0.5}^{1} 2 x d x