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

Lösung

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

\frac{15}{2 ln ( 2 )}

Dezimale

10.82021 \dots

Schritte zur Lösung

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

Vereinfache

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

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

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

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

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

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

Berechne die Grenzen:

\frac{15}{2 ln ( 2 )}

= \frac{15}{2 ln ( 2 )}

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