integral from 0 to e of a^x

解答

\int_{0}^{e} a^{x} d x

\frac{a ^{e} - 1}{ln ( a )}

求解步骤

\int_{0}^{e} a^{x} d x

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

= [\frac{a ^{x}}{ln ( a )}]_{0}^{e}

带入上下限计算后得:

\frac{a ^{e}}{ln ( a )} - \frac{1}{ln ( a )}

= \frac{a ^{e}}{ln ( a )} - \frac{1}{ln ( a )}

化简

= \frac{a ^{e} - 1}{ln ( a )}

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