integral from 0 to 1/7 of xln(7x)

解

\int_{0}^{\frac{1}{7}} x ln (7 x) d x

- \frac{1}{196}

十進法表記

- 0.00510 \dots

解答ステップ

\int_{0}^{\frac{1}{7}} x ln (7 x) d x

部分積分を適用する

= [\frac{1}{2} (x^{2} ln (7 x) - 2 \cdot \int \frac{x}{2} d x)]_{0}^{\frac{1}{7}}

\int \frac{x}{2} d x = \frac{x ^{2}}{4}

= [\frac{1}{2} (x^{2} ln (7 x) - 2 \cdot \frac{x ^{2}}{4})]_{0}^{\frac{1}{7}}

2 \cdot \frac{x ^{2}}{4} = \frac{x ^{2}}{2}

= [\frac{1}{2} (x^{2} ln (7 x) - \frac{x ^{2}}{2})]_{0}^{\frac{1}{7}}

限度を計算する:

- \frac{1}{196}

= - \frac{1}{196}