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

Lösung

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

\frac{30}{ln ( 2 )}

Dezimale

43.28085 \dots

Schritte zur Lösung

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

Vereinfache

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

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

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

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

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

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

Berechne die Grenzen:

\frac{30}{ln ( 2 )}

= \frac{30}{ln ( 2 )}

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