integral from 0 to 1 of 8^x

解答

\int_{0}^{1} 8^{x} d x

\frac{7}{3 ln ( 2 )}

十进制

3.36628 \dots

求解步骤

\int_{0}^{1} 8^{x} d x

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

= [\frac{8 ^{x}}{ln ( 8 )}]_{0}^{1}

化简

ln (8) : 3 ln (2)

= [\frac{8 ^{x}}{3 ln ( 2 )}]_{0}^{1}

带入上下限计算后得:

\frac{7}{3 ln ( 2 )}

= \frac{7}{3 ln ( 2 )}

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