integral from 0 to 3 of 2^{2x}

解答

\int_{0}^{3} 2^{2 x} d x

\frac{63}{2 ln ( 2 )}

十进制

45.44489 \dots

求解步骤

\int_{0}^{3} 2^{2 x} d x

化简

2^{2 x} : 4^{x}

= \int_{0}^{3} 4^{x} d x

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

= [\frac{4 ^{x}}{ln ( 4 )}]_{0}^{3}

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

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

带入上下限计算后得:

\frac{63}{2 ln ( 2 )}

= \frac{63}{2 ln ( 2 )}

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