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人気のある微分積分 >

integral from 0 to 3 of 4^{2x}

解

\int_{0}^{3} 4^{2 x} d x

解

\frac{4095}{4 ln ( 2 )}

+1

十進法表記

1476.95904 \dots

解答ステップ

\int_{0}^{3} 4^{2 x} d x

簡素化

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

= \int_{0}^{3} 1 6^{x} d x

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

= [\frac{1 6 ^{x}}{ln ( 16 )}]_{0}^{3}

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

= [\frac{2 ^{4 x - 2}}{ln ( 2 )}]_{0}^{3}

限度を計算する:

\frac{4095}{4 ln ( 2 )}

= \frac{4095}{4 ln ( 2 )}

グラフ

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