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人気のある微分積分 >

integral from-1 to 0 of x(x^2-1)^{10}

解

\int_{- 1}^{0} x (x^{2} - 1)^{10} d x

解

- \frac{1}{22}

+1

十進法表記

- 0.04545 \dots

解答ステップ

\int_{- 1}^{0} x (x^{2} - 1)^{10} d x

u置換積分法を適用する

= \int_{0}^{- 1} \frac{u ^{10}}{2} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{- 1}^{0} \frac{u ^{10}}{2} d u

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \frac{1}{2} \cdot \int_{- 1}^{0} u^{10} d u

べき乗則を適用する

= - \frac{1}{2} [\frac{u ^{11}}{11}]_{- 1}^{0}

限度を計算する:

\frac{1}{11}

= - \frac{1}{2} \cdot \frac{1}{11}

簡素化

= - \frac{1}{22}

グラフ

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