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人気のある微分積分 >

integral from 0 to 1 of (3t-1)^{50}

解

\int_{0}^{1} (3 t - 1)^{50} d t

解

\frac{2 ^{51} + 1}{153}

+1

十進法表記

1.47176 E 13

解答ステップ

\int_{0}^{1} (3 t - 1)^{50} d t

u置換積分法を適用する

= \int_{- 1}^{2} \frac{u ^{50}}{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}^{2} u^{50} d u

べき乗則を適用する

= \frac{1}{3} [\frac{u ^{51}}{51}]_{- 1}^{2}

限度を計算する:

\frac{2 ^{51}}{51} + \frac{1}{51}

= \frac{1}{3} (\frac{2 ^{51}}{51} + \frac{1}{51})

簡素化

= \frac{2 ^{51} + 1}{153}

グラフ

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