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人気のある微分積分 >

integral from-2 to 6 of x^2\sqrt[3]{x+2}

解

\int_{- 2}^{6} x^{2} 3 x + 2 d x

解

\frac{4752}{35}

+1

十進法表記

135.77142 \dots

解答ステップ

\int_{- 2}^{6} x^{2} 3 x + 2 d x

u置換積分法を適用する

= \int_{0}^{8} (u - 2)^{2} 3 u d u

拡張

(u - 2)^{2} 3 u : u^{\frac{7}{3}} - 4 u^{\frac{4}{3}} + 4 3 u

= \int_{0}^{8} u^{\frac{7}{3}} - 4 u^{\frac{4}{3}} + 4 3 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}^{8} u^{\frac{7}{3}} d u - \int_{0}^{8} 4 u^{\frac{4}{3}} d u + \int_{0}^{8} 4 3 u d u

\int_{0}^{8} u^{\frac{7}{3}} d u = \frac{1536}{5}

\int_{0}^{8} 4 u^{\frac{4}{3}} d u = \frac{1536}{7}

\int_{0}^{8} 4 3 u d u = 48

= \frac{1536}{5} - \frac{1536}{7} + 48

簡素化

\frac{1536}{5} - \frac{1536}{7} + 48 : \frac{4752}{35}

= \frac{4752}{35}

グラフ

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