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人気のある微分積分 >

integral from 0 to 2 of (3t-1)^{56}

解

\int_{0}^{2} (3 t - 1)^{56} d t

解

\frac{5 ^{57} + 1}{171}

+1

十進法表記

4.05783 E 37

解答ステップ

\int_{0}^{2} (3 t - 1)^{56} d t

u置換積分法を適用する

= \int_{- 1}^{5} \frac{u ^{56}}{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_{- 1}^{5} u^{56} d u

べき乗則を適用する

= \frac{1}{3} [\frac{u ^{57}}{57}]_{- 1}^{5}

限度を計算する:

\frac{5 ^{57}}{57} + \frac{1}{57}

= \frac{1}{3} (\frac{5 ^{57}}{57} + \frac{1}{57})

簡素化

= \frac{5 ^{57} + 1}{171}

グラフ

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