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人気のある微分積分 >

integral from 0 to 1/2 of x(1-4x^2)^{10}

解

\int_{0}^{\frac{1}{2}} x (1 - 4 x^{2})^{10} d x

解

\frac{1}{88}

+1

十進法表記

0.01136 \dots

解答ステップ

\int_{0}^{\frac{1}{2}} x (1 - 4 x^{2})^{10} d x

u置換積分法を適用する

= \int_{1}^{0} - \frac{u ^{10}}{8} d u

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

= - \int_{0}^{1} - \frac{u ^{10}}{8} d u

定数を除く:

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

= - (- \frac{1}{8} \cdot \int_{0}^{1} u^{10} d u)

べき乗則を適用する

= - (- \frac{1}{8} [\frac{u ^{11}}{11}]_{0}^{1})

簡素化

= \frac{1}{8} [\frac{u ^{11}}{11}]_{0}^{1}

限度を計算する:

\frac{1}{11}

= \frac{1}{8} \cdot \frac{1}{11}

簡素化

= \frac{1}{88}

グラフ

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