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人気のある微分積分 >

integral from 0 to 2 of 5^{-x}

解

\int_{0}^{2} 5^{- x} d x

解

\frac{24}{25 ln ( 5 )}

+1

十進法表記

0.59648 \dots

解答ステップ

\int_{0}^{2} 5^{- x} d x

u置換積分法を適用する

= \int_{0}^{- 2} - 5^{u} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{- 2}^{0} - 5^{u} d u

定数を除く:

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

= - (- \int_{- 2}^{0} 5^{u} d u)

\int a^{x} d x = \frac{a ^{x}}{ln a}

= - (- [\frac{5 ^{u}}{ln ( 5 )}]_{- 2}^{0})

簡素化

= [\frac{5 ^{u}}{ln ( 5 )}]_{- 2}^{0}

限度を計算する:

\frac{24}{25 ln ( 5 )}

= \frac{24}{25 ln ( 5 )}

グラフ

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