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人気のある微分積分 >

integral from 1 to 4 of 3^{x-1}

解

\int_{1}^{4} 3^{x - 1} d x

解

\frac{26}{ln ( 3 )}

+1

十進法表記

23.66621 \dots

解答ステップ

\int_{1}^{4} 3^{x - 1} d x

簡素化

3^{x - 1} : 3^{x} \cdot 3^{- 1}

= \int_{1}^{4} 3^{x} \cdot 3^{- 1} d x

定数を除く:

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

= 3^{- 1} \cdot \int_{1}^{4} 3^{x} d x

指数の規則を適用する:

a^{- 1} = \frac{1}{a}

= \frac{1}{3} \cdot \int_{1}^{4} 3^{x} d x

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

= \frac{1}{3} [\frac{3 ^{x}}{ln ( 3 )}]_{1}^{4}

限度を計算する:

\frac{78}{ln ( 3 )}

= \frac{1}{3} \cdot \frac{78}{ln ( 3 )}

簡素化

= \frac{26}{ln ( 3 )}

グラフ

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