integral from 1 to 3 of 4^{2x}

解答

\int_{1}^{3} 4^{2 x} d x

\frac{1020}{ln ( 2 )}

十进制

1471.54894 \dots

求解步骤

\int_{1}^{3} 4^{2 x} d x

化简

4^{2 x} : 1 6^{x}

= \int_{1}^{3} 1 6^{x} d x

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

= [\frac{1 6 ^{x}}{ln ( 16 )}]_{1}^{3}

\frac{1 6 ^{x}}{ln ( 16 )} = \frac{2 ^{4 x - 2}}{ln ( 2 )}

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

带入上下限计算后得:

\frac{1020}{ln ( 2 )}

= \frac{1020}{ln ( 2 )}

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