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人気のある微分積分 >

integral from 1 to 2 of t^2ln(t)

解

\int_{1}^{2} t^{2} ln (t) d t

解

- \frac{7}{9} + \frac{8}{3} ln (2)

+1

十進法表記

1.07061 \dots

解答ステップ

\int_{1}^{2} t^{2} ln (t) d t

部分積分を適用する

= [\frac{1}{3} t^{3} ln (t) - \int \frac{t ^{2}}{3} d t]_{1}^{2}

\int \frac{t ^{2}}{3} d t = \frac{t ^{3}}{9}

= [\frac{1}{3} t^{3} ln (t) - \frac{t ^{3}}{9}]_{1}^{2}

限度を計算する:

- \frac{7}{9} + \frac{8}{3} ln (2)

= - \frac{7}{9} + \frac{8}{3} ln (2)

グラフ

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