integral from 2 to 4 of 3^{4x}

解

\int_{2}^{4} 3^{4 x} d x

\frac{10760040}{ln ( 3 )}

十進法表記

9794210.48807 \dots

解答ステップ

\int_{2}^{4} 3^{4 x} d x

簡素化

3^{4 x} : 8 1^{x}

= \int_{2}^{4} 8 1^{x} d x

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

= [\frac{8 1 ^{x}}{ln ( 81 )}]_{2}^{4}

簡素化

ln (81) : 4 ln (3)

= [\frac{8 1 ^{x}}{4 ln ( 3 )}]_{2}^{4}

限度を計算する:

\frac{10760040}{ln ( 3 )}

= \frac{10760040}{ln ( 3 )}