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

Lösung

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

\frac{255}{4 ln ( 2 )}

Dezimale

91.97180 \dots

Schritte zur Lösung

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

Vereinfache

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

= \int_{0}^{2} 1 6^{x} d x

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

= [\frac{1 6 ^{x}}{ln ( 16 )}]_{0}^{2}

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

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

Berechne die Grenzen:

\frac{255}{4 ln ( 2 )}

= \frac{255}{4 ln ( 2 )}

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