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人気のある微分積分 >

integral from 1 to 8 of sqrt(1+81/16 x)

解

\int_{1}^{8} 1 + \frac{81}{16} x d x

解

\frac{2656 83 - 97 194}{486 2}

+1

十進法表記

33.24021 \dots

解答ステップ

\int_{1}^{8} 1 + \frac{81}{16} x d x

u置換積分法を適用する

= \int_{\frac{97}{16}}^{\frac{83}{2}} \frac{16 u}{81} d u

定数を除く:

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

= \frac{16}{81} \cdot \int_{\frac{97}{16}}^{\frac{83}{2}} u d u

べき乗則を適用する

= \frac{16}{81} [\frac{2}{3} u^{\frac{3}{2}}]_{\frac{97}{16}}^{\frac{83}{2}}

限度を計算する:

\frac{83 83}{3 2} - \frac{97 97}{96}

= \frac{16}{81} (\frac{83 83}{3 2} - \frac{97 97}{96})

簡素化

= \frac{2656 83 - 97 194}{486 2}

グラフ

人気の例

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