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人気のある微分積分 >

integral from 0 to 1/2 of xsqrt(1-3x^2)

解

\int_{0}^{\frac{1}{2}} x 1 - 3 x^{2} d x

解

\frac{7}{72}

+1

十進法表記

0.09722 \dots

解答ステップ

\int_{0}^{\frac{1}{2}} x 1 - 3 x^{2} d x

u置換積分法を適用する

= \int_{1}^{\frac{1}{4}} - \frac{u}{6} d u

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

= - \int_{\frac{1}{4}}^{1} - \frac{u}{6} d u

定数を除く:

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

= - (- \frac{1}{6} \cdot \int_{\frac{1}{4}}^{1} u d u)

べき乗則を適用する

= - (- \frac{1}{6} [\frac{2}{3} u^{\frac{3}{2}}]_{\frac{1}{4}}^{1})

簡素化

= \frac{1}{6} [\frac{2}{3} u^{\frac{3}{2}}]_{\frac{1}{4}}^{1}

限度を計算する:

\frac{7}{12}

= \frac{1}{6} \cdot \frac{7}{12}

簡素化

= \frac{7}{72}

グラフ

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