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人気のある微分積分 >

integral from 0 to 1 of (3x+5)^6

解

\int_{0}^{1} (3 x + 5)^{6} d x

解

\frac{673009}{7}

+1

十進法表記

96144.14285 \dots

解答ステップ

\int_{0}^{1} (3 x + 5)^{6} d x

u置換積分法を適用する

= \int_{5}^{8} \frac{u ^{6}}{3} d u

定数を除く:

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

= \frac{1}{3} \cdot \int_{5}^{8} u^{6} d u

べき乗則を適用する

= \frac{1}{3} [\frac{u ^{7}}{7}]_{5}^{8}

限度を計算する:

\frac{2019027}{7}

= \frac{1}{3} \cdot \frac{2019027}{7}

簡素化

= \frac{673009}{7}

グラフ

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